Categories by Kan extension
Topos Berkeley Seminar, 2026-09-08
Slides (PDF)
Keywords: Left Kan extensions, Left Kan calculus, Pra-functors, Pra-comonads, Density comonads, Lawvere theories, Arbitrary product completions, Nerves
Compositional Dynamics in Learning and Mechanics
AFOSR Program Review, 2026-08-06
Slides (PDF)
Keywords: Category theory, Functorial semantics, Operadic syntax for interaction, Adaptive arrangements, Computer systems, Integrators, Gradient descent and backpropagation, Wave and heat equations
Categories by Kan extension
CT 2026, 2026-07-14
Slides (PDF)
Keywords: Left Kan extensions, Left Kan calculus, Pra-functors, Pra-comonads, Density comonads, Lawvere theories, Product completions, Nerves
Accounting for our inventiveness
NITMB Colloquium, 2026-03-17
Slides (PDF) | Video (YouTube)
Keywords: Inventiveness, portability, and compositionality, Mathematical fields as accounting systems, Abiogenesis, Wiring diagrams, Algebras for wiring diagram operads, Polynomial functors, Polynomial coalgebras, Rewiring diagrams and updating interfaces
Achieving answerability
NITMB: Expanding the Palette of Mathematics in Biology, 2026-01-23
Slides (PDF)
An attempt to explain category theory to biologists in 15 minutes
NITMB: Expanding the Palette of Mathematics in Biology, 2026-01-21
Slides (PDF) | Video (YouTube)
Keywords: Operations and relations, Popper's objection, Operads, Hierarchical protein materials, Wiring diagrams, Algebras
The double category Int(Poly_+) models control flow and data flow
Topos Berkeley Seminar, 2025-07-15
Outline (PDF)
Language and substrates: Dependent type theory and topological spaces
AFOSR Program Review, 2025
Slides (PDF)
Keywords: Formal effects in material contexts, Categories, functors, and natural transformations, Monoidal structures, monoids, and comonoids, Monads and comonads, Algebraic theories, Dependent type theory, Categories as comonads, Topological intuition for comonads
Plausible Fiction: Tending Actualizes Potential
MIT CEE: ACT4ED, 2024-12-02
Slides (PDF) | Video (YouTube)
Keywords: Plausible fiction, Care tends to actualize potential, Lightning, hurricanes, and life, Recombination and coordination in life, Working language, Accounting systems, Petri nets, Operadic gap-filling
Plausible Fiction: Accounting for Actualizing Potential
IPAM Naturalistic Approaches to AI, 2024-11-05
Slides (PDF) | Video (YouTube)
Keywords: Plausible fiction, Care tends to actualize potential, Lightning, hurricanes, and life, Recombination and coordination in life, Working language, Accounting systems, Petri nets, Accounting for ourselves
How should one govern a plausible fiction platform?
MathGov, 2024-10-09
Outline (PDF)
Structure and Dynamics of Working Language
AFOSR Program Review, 2024-08-29
Slides (PDF)
Keywords: Polynomial functors, Categories, functors, and natural transformations, Endofunctors and monoidal structures, Monoids and comonoids, Monads and comonads, Substitution product, Free monad monad and cofree comonad comonad
``All my relations'' Contributing to a fabric of belonging
AGI 2024, 2024-08-15
Slides (PDF) | Video (YouTube)
Keywords: Collective sensemaking, Tracking what we care about, Abstraction, Category theory, Relational math, Interfaces, Delegation, Dynamic arrangements
The Polynomial Abacus
FMCS 2024, 2024-07-09
Slides (PDF)
Keywords: Abacus, Polynomials, Poly, Monoidal structures, Comonoids, Bicomodules, Wiring diagrams, Categorical databases
Pattern runs on matter: The free monad monad as a module over the cofree comonad comonad
ACT 2024, 2024-06-17
Slides (PDF)
Keywords: Polynomial functors, Moore and Mealy machines, Wiring diagrams, Free monad, Cofree comonad, Tree representation, Monad monad and Comonad comonad, Interactions between free and cofree
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Princeton Neuroscience of Cognitive Control and Astera, 2024-04-17
Slides (PDF)
Keywords: Interfaces as polynomials, Semantics of polynomial operations, Arrangements, Dynamic arrangements, Digital circuits and control systems, Deep learning, Organizational structures, Active inference
Applied Category Theory: Towards a hard science of interdisciplinarity
Princeton Neuroscience of Cognitive Control and Astera, 2024-04-10
Slides (PDF)
Keywords: Mathematical fields as accounting systems, Category theory, Operads, Wiring diagrams, Probabilities, Deep learning, Dynamic arrangements, Dynamic operads
How can math promote life?
Annual Mathematics and Philosophy Lecture, University of Calgary, 2024-03-07
Slides (PDF)
Keywords: Accountability, Mathematical fields as accounting systems, Interfaces, Algebraic operations on interfaces, Nesting arrangements, Dynamics, Dynamic arrangements, Recombinant intelligence
Category Theory in Science and Engineering
Caltech, Special Seminar in Mechanical and Civil Engineering, 2023-12-14
Slides (PDF)
Keywords: Mathematical fields as accounting systems, Category theory, Operads, Wiring diagrams, Manifolds, Lenses and open dynamical systems, Dynamic arrangements, Compositional physics
Applied Category Theory: Towards a hard science of interdisciplinarity
Chevron Systems Engineering Community of Practice, 2023-10-11
Slides (PDF)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Probabilities, Deep learning, Prediction markets, Organizations, Dynamic operads
Dynamic operads: Compositional adaptive systems
AFOSR Program Review, 2023-09-14
Slides (PDF)
Keywords: Categorical systems theory, Compositional adaptive systems, Mathematics of interfaces, Dynamic operads, Compositional physics, Lie groups, Hopf monoids
All concepts are Cat^#
Applied Category Theory 2023, 2023-08-04
Slides (PDF)
Keywords: Poly, Polynomial comonads, Cat^#, Categories, Span, Multisorted polynomials, Dynamic functions, Dynamic arrangements
Applied Category Theory: Towards a hard science of interdisciplinarity
Society for Multidisciplinary and Fundamental Research, Interdisciplinary School, 2023-07-25
Slides (PDF) | Video (YouTube)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Probabilities, Deep learning, Prediction markets, Organizations, Dynamic operads
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Category Theory for Consciousness Science, 2023-04-16
Slides (PDF) | Video (YouTube)
Keywords: Accounting, Dynamic organizational systems, Sense-making, Polynomial morphisms, Moore machines, Wiring diagrams, Artificial neural networks, Prediction markets
Dynamic organizational systems: From deep learning to prediction markets
Categories for AI, 2023-03-23
Slides (PDF) | Video (YouTube)
Keywords: Dynamic organizational systems, Polynomial morphisms, Comonoids, Lenses, Moore machines, Wiring diagrams, Artificial neural networks, Prediction markets
The Microservices Operad –OR– the free monad monad is a module over the cofree comonad comonad
Topos Berkeley Seminar, 2023-02-21
Outline (PDF)
Poly is an unreasonably effective abstraction; Might it relate to healthy systems?
Finding the Right Abstractions for Healthy Systems, 2023-01-09
Slides (PDF)
Keywords: Poly, Comonoids, Lenses, Moore machines, Mealy machines, Wiring diagrams, Databases and data migration, Dynamic organizational systems
Category theory is living language
Joint Mathematics Meetings, Special Session on Applied Category Theory, 2023-01-05
Slides (PDF)
Keywords: Accounting systems, Working language, Matter and pattern, Compositionality, ACT, Spencer's graph
Effects Handlers and Bicomodules
Topos Berkeley Seminar, 2022-12-12
Outline (PDF)
What are we tracking? How category theory puts thinking on rails
NIST, Compositional Structures in Systems Engineering and Design Workshop, 2022-11-03
Slides (PDF)
Keywords: Tracking values, Accounting systems, Finding the right abstractions, Recipes, Recipe structure, Ologs, Databases, Categorical imperative
Dynamic organizational structures
NASA Prebiotic Chemistry and Evolution on the Early Earth (PCE3), 2022-10-20
Slides (PDF)
Keywords: Mathematical fields as accounting systems, Dynamic organizational structures, Open dynamical systems, Wiring diagrams and interaction patterns, Mode dependent interaction, Applications to PCE3
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Active Inference Institute, 2022-09-13
Slides (PDF) | Video (YouTube)
Keywords: Interfaces as polynomials, Arrangements, Dynamics, Dynamic arrangements, Digital circuits and control systems, Deep learning, Dynamic organizational structures, Active inference
Is Poly the true language of computation?
AFOSR Program Review, 2022-08-11
Slides (PDF)
Keywords: Algebraic structure of complex systems, Category theory, Mode dependent interaction, Poly, Natural applications of Poly, Design environment
Polynomial Functors and Shannon Entropy
ACT 2022, 2022-07-19
Slides (PDF)
Keywords: Polynomial functors, Entropy, Morphisms of polynomials, Fundamental invariants, Distributive monoidal structures, Derivatives, Bifibrations, Categorical partition function
The free monad, cofree comonad, and topological space associated to a polynomial
Topos Institute, Berkeley Seminar, 2022-06-14
Outline (PDF)
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Allen Discovery Center, 2022-06-07
Slides (PDF) | Video (YouTube)
Keywords: Interfaces, Polynomial functors, Arrangements, Dynamics, Digital circuits, Control systems, Deep learning, Morphogenesis of systems
Polynomial Functors and Shannon Entropy
Symposium on Categorical Semantics of Entropy, 2022-05-13
Slides (PDF) | Video (YouTube)
Keywords: Polynomial functors, Entropy, Morphisms of polynomials, Fundamental invariants, Distributive monoidal structures, Derivatives, Bifibrations, Categorical partition function
Some applications of polynomial functors
University of Pisa, Computer Science Department, 2022-04-06
Slides (PDF)
Keywords: Polynomial functors, Lens pattern, Polymorphic data types, Algebraic datatypes, Dynamical systems, Mealy machines, Wiring diagrams, Categorical databases
Functorial Aggregation
Workshop on Polynomial Functors, 2022-03-18
Slides (PDF) | Video (YouTube)
Keywords: Categorical databases, Aggregation, Poly, Dirichlet product, Substitution product, Cat^#, Database schemas, Prafunctors
Sense-making: accounting for intelligibility
Mathematics of Collective Intelligence, 2022-02-19
Slides (PDF)
Keywords: Accounting systems, Collective intelligence, Sense-making, Operads, Interaction patterns, Interacting dynamical systems, Governance, Accountability
Categorical Interaction in the Polynomial Ecosystem
Seminar on Categorical Interaction, 2022-01-25
Slides (PDF)
Keywords: Polynomial functors, Lens pattern, Dynamical systems, Wiring diagrams, Interaction patterns, Categorical databases, Open games, Deep learning
Learners' languages
Topos Internal Seminar, 2021-09-21
Slides (PDF)
Keywords: Poly, Monoidal structures, Internal hom, Coalgebras, Interaction patterns, Wiring diagrams, Characters, Organizations
Dynamic networks and learning
AFOSR Program Review, 2021-04-16
Slides (PDF)
Keywords: Complex systems theory, Dynamic networks, Bundles, Lenses, Open dynamical systems, Wiring diagrams, Operadic composition, Deep learning
The Polynomial Abacus
Workshop on Polynomial Functors, 2021-03-15
Slides (PDF) | Video Part 1 | Video Part 2
Keywords: Poly, Monoidal structures, Comonoids, Cofree comonoids, Bicomodules, Moore machines, Wiring diagrams, Categorical databases
Polynomials and the dynamics of data
Seminario de categorias UNAM, 2021-02-17
Slides (PDF) | Video (YouTube)
Keywords: Poly, Polynomial morphisms, Monoidal structures, Comonoids, Bicomodules, Moore machines, Wiring diagrams, Categorical databases
Poly: a category of remarkable abundance
Topos Colloquium, 2021-02-04
Slides (PDF) | Video (YouTube)
Keywords: Poly, Monoidal structures, Comonoids, Bicomodules, Moore machines, Wiring diagrams, Categorical databases, Cellular automata
Applied Category Theory: Mathematics for Interdisciplinary systems modeling
PNNL, 2021-02-02
Slides (PDF)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Probabilities, Grammars, Recipes, Tensor networks, Smart grid
A Tutorial on Category theory: Part 1: pure and classical
Finding the Right Abstractions, Topos Institute, 2021
Slides (PDF)
Keywords: Sets, Orders, Universal properties, Categories, Initial and terminal objects, Coproducts and products, Functors, String diagrams
Cultivating Strategies
Finding the Right Abstractions, Topos Institute, 2021
Slides (PDF)
Keywords: Strategies, Negentropy, AI transition, Collective intelligence, Dynamical systems, Organizations, Polynomial functors, Empowerment
Addressing hypercomplexity: The ACT pipeline from abstraction to application
AFOSR Program Review, 2020-08-04
Slides (PDF)
Keywords: Applied category theory, Hypercomplexity, ACT pipeline, Robotics, Temporal type theory, Stochastic processes, Petri nets, Wiring diagrams
Poly: an abundant categorical setting for mode-dependent dynamics
ACT 2020, 2020-07-07
Slides (PDF)
Keywords: Polynomials, Adjunctions, Bimorphic lenses, Monoidal structures, Moore machines, Wiring diagrams, Mode-dependent dynamics, Comonoids
Polynomials: from dynamics to databases
Tallinn CS Theory Seminar, 2020-06-25
Slides (PDF)
Keywords: Polynomials, Monoidal structures, Moore machines, Wiring diagrams, Mode-dependent dynamics, Comonoids, Databases, Data migration
``All my relations'' Contributing to a fabric of belonging
AGI 2020, 2020-06-12
Slides (PDF)
Keywords: Collective sensemaking, Care, Abstraction, Category theory, Interfaces, Delegation, Machines, Dynamic arrangements
Internal probability valuations
Categorical Probability and Statistics, 2020-06-07
Slides (PDF)
Keywords: Stochastic processes, Sheaves, Topos logic, Modalities, Internal topological spaces, Internal real numbers, Probability valuations, Families of valuations
Polynomial functors II: Seven wonders of the composition product
MIT Categories Seminar, 2020-05-28
Slides (PDF)
Keywords: Polynomials, Composition product, Strategies, Comonoids, Dynamical systems, Operads, Categories, Bimodules
Mode dependent dynamical systems and polynomial functors
MIT, 2020-03-05
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
ETH Zurich, 2019-09-25
Slides (PDF)
Keywords: Operads, Wiring diagrams, Functors, Operad algebras, Tensor networks, Dynamical systems, Smart grid
Monadic decision processes and hierarchical planning for autonomous systems
AFOSR Program Review, 2019-08-20
Slides (PDF)
Keywords: Autonomous systems, Hierarchical planning, Markov decision processes, Monads, Monadic MDPs, Combining planners
Graphical abelian logic
ACT 2019, 2019-07-19
Slides (PDF)
Keywords: Graphical languages, Abelian categories, Abelian relations, Po-props, Functors, Finitely-generated abelian groups, Monoidal functors
Graphical abelian logic
CT 2019, 2019-07-11
Slides (PDF)
Keywords: Abelian categories, Graphical languages, Abelian relations, Finitely-generated abelian groups, Syntactic category, Supply, Abelian calculi, Predicates
Autopoiesis, Cognition, and Evolution
AFOSR Program Review, 2019-06-26
Slides (PDF)
Keywords: Autopoiesis, Cognition, Distributed cognition, Wiring diagrams, Dynamical systems, Mode-dependent networks
Reglog -- the game
Compose Conference, 2019-06-24
Slides (PDF) | Video (YouTube)
Keywords: Regular logic, Compositionality, Regular categories, Graphical regular logic, Wiring diagrams, Graphical calculi, Categorical Query Language
Monadic Decision Processes for Hierarchical Planning
MIT CT Seminar, 2019-05-23
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
Oxford, Future of Humanity Institute, 2019-05-09
Slides (PDF)
Keywords: Compositionality, Operads, Wiring diagrams, Protein materials, Probabilities, Grammars, Recipes, Dynamical systems
Applied Category Theory: Mathematics for Interdisciplinary systems modeling
MIT ASO, 2019-05-09
Slides (PDF)
Keywords: Operads, Wiring diagrams, Protein materials, Probabilities, Functors, Algebras, Dynamical systems, Tensor networks
Applied Category Theory: Towards a science of interdisciplinarity
Bridgewater, 2019-05-09
Slides (PDF)
Keywords: Compositionality, Operads, Wiring diagrams, Protein materials, Probabilities, Categories, Database schemas, Categorical Query Language
Categorical Databases
Uber, 2019-04-22
Slides (PDF)
Keywords: Information integration, Database schemas, Categories, Functors, Functorial data migration, Grothendieck construction, RDF, Categorical Query Language
Reglog -- the game
MIT ACT Seminar, 2019-04-11
Slides (PDF)
Keywords: Regular logic, Compositionality, Regular categories, Graphical regular logic, Wiring diagrams, Graphical calculi, Categorical Query Language
Applied Category Theory: Towards a science of interdisciplinarity
UT Austin, 2019-03-11
Slides (PDF)
Keywords: Compositional operations, Wiring diagrams, Hierarchical protein materials, Probabilities, Grammars, Tensor networks, Dynamical systems, Smart grid
Categorical Databases
Moderna, 2019-02-27
Slides (PDF)
Keywords: Information integration, Information kinematics, Databases, Categories, Functors, Functorial data migration, Grothendieck construction
Categorical Databases
Kensho, 2019-02-27
Slides (PDF)
Keywords: Information integration, Information kinematics, Databases, Categories, Functors, Functorial data migration, Grothendieck construction
Petri Banks, quiver representations, and control
MIT, 2019-01-10
Outline (PDF)
Categorical Databases
BAE Systems, 2019-01-09
Slides (PDF)
Keywords: Information integration, Information kinematics, Databases, Categories, Functors, Functorial data migration
Lenses: applications and generalizations
UC Riverside, 2019
Slides (PDF)
Keywords: Agent/environment systems, Lenses, Wiring diagrams, Dynamical systems, Learners, Hierarchical planning, Bundles, Polynomial functors
Graphical calculus for abelian categories
MIT CT Seminar, 2019
Outline (PDF)
Lenses: applications and generalizations
MIT, 2019
Slides (PDF)
Keywords: Agent/environment systems, Lenses, Wiring diagrams, Dynamical systems, Learners, Hierarchical planning, Bundles, Polynomial functors
Graphical presentations of abelian categories
McGill University, 2019
Outline (PDF)
String diagrams for regular logic
Octoberfest, 2018-10-27
Slides (PDF)
Keywords: String diagrams, Adjunctions, Regular hypergraph categories, Regular categories, Regular logic, Cospan-algebras
Some categorical perspectives on institutions
MIT, 2018-10-01
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
Institute of Systems Research, UMD, 2018-09-28
Slides (PDF)
Keywords: Category theory, Compositional operations, Operads, Wiring diagrams, Operad algebras, Tensor networks, Dynamical systems, Interdisciplinarity
Double categories
MIT Applied CT Seminar, 2018-08-23
Outline (PDF)
Decomposition spaces and toposes
MIT CT Seminar, 2018-07-19
Outline (PDF)
A topos-theoretic approach to systems and behavior
Category Theory Conference, 2018-07-09
Slides (PDF)
Keywords: Behavior, Topos, Discrete vs. continuous time, Temporal logic, Internal language of a topos, Dedekind numeric objects, Temporal type theory, Differential equations
Backprop as Functor: A compositional perspective on supervised learning
Max Planck Institute, 2018-05-06
Outline (PDF)
A higher-order temporal logic for dynamical systems
Applied Category Theory Workshop, Lorentz Center, 2018-05-02
Slides (PDF) | Video (YouTube)
Keywords: Hypergraph categories, Topos, Type theory, Kripke-Joyal semantics, Dedekind numeric objects, Modalities, Differential equations, Behavior contracts
Discrete temporal type theory
MIT CT Seminar, 2018-04-26
Outline (PDF)
Categorical views of regular, coherent, geometric logic: from classical to wiring-theoretic
MIT, 2018-04-12
Outline (PDF)
Intuition/Talk on String diagrams for traced and compact categories are oriented 1-cobordisms
Toposes in Como, 2018-03-16
Outline (PDF)
A higher-order temporal logic for dynamical systems
NIST Applied Category Theory Workshop, 2018-03-16
Slides (PDF)
Keywords: Hypergraph categories, Relations in a topos, Topos, Type theory, Kripke-Joyal semantics, Differential equations, Behavior contracts
A topos-theoretic approach to systems and behavior
CMU, 2018-03-16
Slides (PDF)
Keywords: Behaviors as sheaves, Topos, Discrete vs. continuous time, Temporal logic, Internal language of a topos, Temporal type theory, Differential equations, Behavior contracts
A higher-order temporal logic for dynamical systems
Barcelona, 2018-03-16
Slides (PDF)
Keywords: Hypergraph categories, Relations in a topos, Toposes, Type theory, Kripke-Joyal semantics, Differential equations, Behavior contracts
A higher-order temporal logic for dynamical systems
AFOSR Program Review, 2018-03-16
Slides (PDF)
Keywords: Behavior types, Interconnection of behaviors, Toposes, Logic, Intervallic monitors, Logic of behavior types, HOTL, Behavior contracts
Metric realization of fuzzy simplicial sets
MIT Applied CT Seminar, 2018-02-22
Outline (PDF)
Backprop as Functor: A compositional perspective on supervised learning
Oxford OASIS, 2018-02-01
Outline (PDF)
Learning relations via adjunctions
MIT CT Seminar, 2018
Outline (PDF)
Some Applications of Category Theory
Salem State University, 2017-12-12
Slides (PDF)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Grammars, Recipes, Open dynamical systems, Relations, Tensors
A higher-order temporal logic for dynamical systems
AMS Fall Sectional, Riverside CA, 2017-11-04
Slides (PDF)
Keywords: Hypergraph categories, Relations in a topos, Toposes, Type theory, Kripke-Joyal semantics, Modalities, Differential equations, Behavior contracts
Cayley graphs and the Grothendieck construction
Harvard Math Table, 2017-10-24
Outline (PDF)
Category theory in science and engineering: A framework for information integration
MIT, 2017-10-02
Slides (PDF)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Grammars, Recipes, Tensors, Equations, Compositional mappings
Machine learning and category theory: perception and cognition
McGill Applied Mathematics Seminar, 2017-10-02
Slides (PDF)
Keywords: Operads, Wiring diagrams, Hierarchical protein materials, Grammars, Recipes, Equations, Clustering, Open dynamical systems
Using category theory for information integration
Caltech, AMBER Lab Seminar, 2017-10-02
Slides (PDF)
Keywords: Information integration, Operads, Wiring diagrams, Algebras of operads, Equations, Dynamical systems, Compositional mappings, Bifurcation diagrams
Language and semantics for behavior
MIT CT Seminar, 2017-09-05
Outline (PDF)
The Pixel Array method for solving nonlinear systems
SIAM, 2017-07-13
Slides (PDF)
Keywords: Pixel Array method, Nonlinear systems, Array multiplication, Equations, Wiring diagrams
Compositional contracts for hybrid dynamical systems
SIAM, Novel Approaches for Systems of Systems, 2017-07-12
Slides (PDF)
Keywords: Composition, Behavior contracts, Behavior types, Sheaves, Topos theory, Modalities, Hybrid dynamical systems, National airspace system
Compositional analyses of dynamical systems
AFOSR Program Review, USAF Academy, 2017-06-28
Slides (PDF)
Keywords: Composition, Operads, Wiring diagrams, Compositional mappings, Dynamical systems, Bifurcation diagrams, Steady states, Discretization
“How do these things compose?” Modularity in materials, databases, and dynamical systems
AFOSR Program Review, USAF Academy, 2017-06-28
Slides (PDF)
Keywords: Composition, Operads, Wiring diagrams, Mode-dependent wiring diagrams, Bifurcation theory, Evolution and learning, Recipes
An Operadic Approach to Compositionality
UAB Topology Seminar, Barcelona, 2017-06-12
Slides (PDF)
Keywords: Compositionality, Operads, Wiring diagrams, String diagrams, Monoidal categories, Hypergraph categories, Dynamical systems, Hierarchical protein materials
Sheaf-theoretic analysis of networked dynamical systems
Emerging Topics in Network Dynamical Systems, Lorentz Center, 2017-06-08
Slides (PDF)
Keywords: Interfaces, Wiring diagrams, Networks, Behaviors, Sheaves, Topos, Contracts, Safety properties
Categorical databases
Broad Institute, 2017-03-29
Slides (PDF)
Keywords: Functors, Categories, Database schemas, Data migration, Adjoints, Views, FQL, Grothendieck construction
The pixel array method for solving non-linear systems of equations
MIT Mathematics IAP Lecture Series, 2017-01-30
Slides (PDF)
Keywords: Wiring diagrams, Array multiplication, Boolean matrices, Clustering, Dynamical systems, PDEs, Heat equation, Open dynamical systems
Notes for LambdaConf
LambdaConf, 2017
Outline (PDF)
An Operadic Approach to Compositionality
Compositionality Workshop, Simons Institute for the Theory of Computing, 2016-12-05
Slides (PDF)
Keywords: Composition, Syntax and semantics, String diagrams, Operads, Traced monoidal categories, Hypergraph categories, Dynamical systems, Wiring diagrams
A whirlwind tour of category theory, for the working scientist and engineer
Telecom Bretagne, 2016-11-10
Slides (PDF)
Keywords: Categorification, Finite sets, Functors, Database schemas, Posets, Monoids, Groups, Sheaves
The Pixel Array method for nonlinear systems, and applications to numerical PDEs
Telecom Bretagne, 2016-11-10
Slides (PDF)
Keywords: Wiring diagrams, Array multiplication, Boolean matrices, Clustering, PDEs, Heat equation, Open dynamical systems, Plotting
The Pixel Array method for nonlinear systems, and applications to numerical PDEs
MIT Numerical Methods for PDE Seminar, 2016-10-26
Slides (PDF)
Keywords: Wiring diagrams, Array multiplication, Boolean matrices, Clustering, Cluster trees, Numerical methods for PDEs, Open dynamical systems, Pixel Array analysis
A whirlwind tour of category theory, for the working scientist and engineer
Sandia National Labs, 2016-10-04
Slides (PDF)
Keywords: Category theory, Functors, Categorification, Database schemas, Data migration, Posets, Monoids, Sheaves
Air Force Research Laboratory, Dayton, 2016-06-29
Pixel matrices for big, messy, real-world data
5th Mini-Symposium on Computational Topology, SoCG, 2016-06-15
Outline (PDF)
Calculating steady states of nonlinear dynamical systems using matrix arithmetic
Binghamton University Mathematics Colloquium, 2016-04-07
Outline (PDF)
Operads as a potential foundation for systems of systems
Mathematical Biosciences Institute, The Ohio State University, 2016-03-22
Slides (PDF)
Keywords: Operads, System composition, Feedforward composition, Feedback composition, Dynamical systems, Context-free grammars, Port graphs, Compositional mappings
Bifurcation theory of networked dynamical systems
SIAM (did not occur), 2016
Outline (PDF)
A topos-theoretic approach to systems and behavior
Toposes in Como, 2016
Slides (PDF)
Keywords: Sheaves, Temporal type theory, Topoi, Temporal logic, Differential equations, Behavior contracts, Dedekind numeric objects, Discrete vs. continuous time
Category Theory 2016, 2016
Outline (PDF)
Operads: a mathematical approach to compositionality (Extended Abstract)
NIST Computational Category Theory Workshop, 2015-10-28
Outline (PDF)
Operadics: the mathematics of modular design
NIST, 2015-06-17
Slides (PDF)
Keywords: Operads, Applied category theory, Wiring diagrams, Protein materials, Matriarch, Databases, Open dynamical systems, Electrical circuits
Protein materials architecture by design
NIST, 2015-06-16
Slides (PDF)
Keywords: Hierarchical protein materials, Matriarch, Materials architecture, Operads, Wiring diagrams, Category theory, Open dynamical systems, Electrical circuits
Operads as a language for modular design
FMCS 2015, 2015-06-05
Slides (PDF)
Keywords: Materials architecture, Modular systems, Operads, Operad algebras, Wiring diagrams, String diagrams, Traced categories, Matriarch
Thinking about modularity in networks
University of Pennsylvania, Complex Systems Seminar, 2015-04-03
Slides (PDF)
Keywords: Operads, Recipes, Networks, Materials design, Matriarch, Materials architecture, Wiring diagrams
A mathematical language for modular systems
AFOSR Program Review, 2015-01-29
Slides (PDF)
Keywords: Materials architecture, Modular systems, Operads, Operad algebras, Wiring diagrams, String diagrams, Traced categories, Matriarch
A category-theoretic approach to materials design
8th Design Theory SIG Paris Workshop, 2015-01-26
Slides (PDF)
Keywords: Materials design, Materials architecture, Operads, Artifact theories, Matriarch, Category theory, Wiring diagrams, Context-free grammars
A networked world
Workshop in Turin, 2015
Outline (PDF)
Category theory, the theory of mathematical structures: a whirlwind tour
MIT LIDS, 2015
Outline (PDF)
Notes on Applied category theory: Information structures and modular systems
Ecole Polytechnique Federale de Lausanne, 2015
Outline (PDF)
Category Theory -- A Formal and Flexible Interdisciplinary Language
Institute for Advanced Study, 2014-03-20
Outline (PDF)
Categorical databases
Amgen, 2014-03-04
Slides (PDF)
Keywords: Categories, Functors, Database schema, Data migration, Adjoints, FQL, Grothendieck construction, RDF
Categorical databases
PARC, 2014-03-03
Slides (PDF)
Keywords: Categories, Functors, Database schema, Data migration, Adjoints, FQL, Grothendieck construction, RDF
Categorical databases
Oracle, 2014-02-28
Slides (PDF)
Keywords: Databases as languages, Category theory, Relational databases, Schemas as categories, Functorial Query Language, Data Exchange, RDF, Data migration functors
Operads, and their algebras, for building new processors from old
UIUC, 2014-02-25
Outline (PDF)
Wiring diagrams and state machines
MIT, 2014-02-19
Slides (PDF)
Keywords: Wiring diagrams, Tensor products, Symmetric monoidal categories, Lax monoidal functors, State machines, State reduction, Linear combinations monad, Linear machines
Toward a categorical foundation of functional reactive programming
MIT, 2014-02-19
Slides (PDF)
Keywords: Functional reactive programming, Wiring diagrams, Tensor products, Safe wiring diagrams, Symmetric monoidal categories, Lax monoidal functors, State propagators, State reduction
Toward a categorical foundation of functional reactive programming
MIT, 2014-02-19
Slides (PDF)
Keywords: Functional reactive programming, Wiring diagrams, Tensor products, Symmetric monoidal categories, Lax monoidal functors, State propagators, State reduction, Linear propagators
Toward a categorical foundation of functional reactive programming
MIT (PLV Lunch), 2014-02-19
Slides (PDF)
Keywords: Functional reactive programming, Wiring diagrams, Tensor products, Safe wiring diagrams, Symmetric monoidal categories, Lax monoidal functors, State propagators, State reduction
Toward a categorical foundation of functional reactive programming
Harvard University, 2014-02-19
Slides (PDF)
Keywords: Functional reactive programming, Wiring diagrams, Tensor products, Safe wiring diagrams, Symmetric monoidal categories, Lax monoidal functors, State propagators, State reduction
Categorical databases
Amgen, 2014-02-19
Slides (PDF)
Keywords: Categories, Functors, Database schemas, Set-valued functors, Functorial data migration, FQL, Grothendieck construction, RDF
Toward a categorical foundation of functional reactive programming
Carnegie Mellon University, 2014-01-23
Slides (PDF)
Keywords: Functional reactive programming, Wiring diagrams, Tensor products, Symmetric monoidal categories, Lax monoidal functors, State propagators, State reduction, Monads
Toward a mathematical science of informatics
Office of Naval Research Review, 2013-09-18
Slides (PDF)
Keywords: Information structures, Databases, Categories, Functors, Functorial data migration, FQL, Grothendieck construction, RDF
Toward a mathematical science of informatics
National Institute of Standards and Technology, 2013-06-13
Slides (PDF)
Keywords: Information structures, Databases, Ologs, Categories, Functors, Functorial data migration, FQL, RDF
Title: Lifting problems and data
MathFest, 2012-08-04
Slides (PDF)
Keywords: Databases, Database schemas, Set-valued functors, Functorial data migration, Category of elements, RDF, Lifting problems, Queries
Categorical ontologies and databases
Stanford Center for Biomedical Research, 2012-07-26
Slides (PDF)
Keywords: Categories, Functors, Database schemas, Set-valued functors, Functorial data migration, Grothendieck construction, RDF, Lifting problems
A categorical approach to high-assurance science
Office of Naval Research, 2012-06-13
Slides (PDF)
Keywords: Sheaves, Databases, Category theory, Ologs, Fiber products, Functors, Data migration, Hierarchical categories
Categorical databases
Amgen, 2012-01-24
Slides (PDF)
Keywords: Category theory, Functors, Data migration, Adjoints, Views, Grothendieck construction, RDF, Queries
Categorical databases
Johnson & Johnson, 2012-01-13
Slides (PDF)
Keywords: Category theory, Functors, Data migration, Adjoints, Views, Grothendieck construction, RDF, Queries
Categorical databases
MIT, 2012-01-13
Slides (PDF)
Keywords: Category theory, Functors, Data migration, Adjoints, Views, Grothendieck construction, RDF, Queries
Categorical databases
Special Geometry Seminar, UT Austin, 2012
Outline (PDF)
Categorical databases
Carnegie Mellon University, 2011-01-18
Slides (PDF)
Keywords: Category theory, Functors, Data migration, Adjoints, Views, Grothendieck construction, RDF, Queries
Categorical Information Theory
MSS Colloquium, UIUC, 2011
Outline (PDF)
Categorical Information Theory
Topology Seminar, JHU, 2011
Outline (PDF)
Databases are categories
Harvard University, 2010-11-03
Slides (PDF)
Keywords: Categories, Functors, Databases, Grothendieck construction, RDF, Data migration, Views, Provenance
Databases are Categories II
Galois, 2010-10-22
Slides (PDF)
Keywords: Information schemas, Sketches, Sketch maps, RDF triple stores, Data migration, Sigma and Pi functors, Polynomial functors, Ologs
Databases = Categories
MIT CSAIL, 2010-09-16
Slides (PDF)
Keywords: Foreign keys, Categorical normal form, Schema morphisms, Pullback, Existential and universal push-forwards, Joins and unions, Relational model, M-sets
Communication networks
MIT Linguistics, Semantics Reading Group, 2010-09-15
Outline (PDF)
Databases are Categories II
Galois, 2010-06-03
Slides (PDF)
Keywords: Information schemas, Sketches, Sketch maps, RDF triple stores, Data migration, Sigma and Pi functors, Polynomial functors, Ologs
Topology and information
University of Chicago, 2010
Outline (PDF)
Mapping spaces in quasi-categories
University of Oregon, 2009-11-07
Slides (PDF)
Keywords: Homotopy theory, Model structures, Homotopy function complex, Quillen equivalence, Weak Kan complexes, Mapping spaces, Necklaces