Discrete vs. filtered accessibility and presentability
2026-09-24
Coproduct-based analogues of accessibility, still good for computing hom-sets.
Who cares about a computation?
2026-09-22
Can computers care, and does care need an accounting system?
Neural wiring diagrams for message passing in multiscale organizations
2024-11-08
Neural wiring diagrams as a message-passing language for task delegation.
Plausible fiction
2024-08-27
Shared imaginative fictions as a way to steer a troubled world.
A polynomial account of Bayesian update (with Sophie Libkind)
2024-08-12
Making sense of Bayesian update using polynomial functors.
Poly @ Work 2024 (with Sophie Libkind)
2024-03-27
Report on the 2024 workshop on polynomial functors.
Poly-morphic effect handlers (with Harrison Grodin)
2024-01-03
Composable effect handlers via polynomial functors and free monads.
Solving problem-solving (with Priyaa Varshinee Srinivasan)
2023-11-13
Problem-solving as translation between abstractions, via category theory.
Lie groups induce Hopf monoids in Poly
2023-10-26
Cotangent bundles of Lie groups give Hopf monoids in Poly.
Powers of polynomial monads
2023-09-21
Exponentiating polynomial monads is lax monoidal in two ways.
A nuclear adjunction between Poly and Dir
2023-07-21
An adjunction relating forward-forward and forward-backward bundle maps.
Dialogue on a mathematical approach to the good (with Bartłomiej Skowron and David Corfield)
2023-07-11
Dialogue on what mathematics and ethics have in common.
Natural transformations between cofunctors
2023-05-26
A clean formula for natural transformations between cofunctors.
Spooling out syntax from behavior
2023-04-24
Extracting free-monad syntax from the behavior of dynamical systems.
Lotteries: a constructive version of the distributions monad
2023-03-23
A polynomial lotteries monad, compared with the distributions monad.
Category theorists welcome self-learners in a new outreach panel (with Alexis Anaya)
2023-03-09
Announcing a category theory outreach panel for self-learners.
Promonoidal categories and wiring diagrams
2023-01-31
Wiring diagram operads are promonoidal, so operations can be factored.
Lenses are semi-monads, maybe lenses are monads
2022-12-20
A semi-monad on lenses, for speeding up wiring diagram boxes.
Where matter and pattern meet
2022-11-07
Where matter meets pattern: language, compositionality, and category theory.
When you light up, I light up (with Sophie Libkind)
2022-10-28
Hebbian learning modeled as a dynamic monoidal category.
Nate & Jesse’s adjoint 5-tuple
2022-09-29
A chain of five adjoints wanted for a type theory.
It’s Proly like Poly but better
2022-08-04
Proly: a less discrete, richer cousin of Poly.
A 15-year history of my research program, in 10 minutes
2022-07-07
Video overview of my applied category theory research since 2007.
Graphs in Poly
2022-06-16
Graphs in Poly, building intuition for comonoids as categories.
An account of sense-making (with James Dama)
2022-06-03
Are making sense and having senses fundamentally the same?
The “artificial” distinction
2022-05-18
Questioning whether the natural/artificial distinction makes sense.
Co-design of dynamical systems
2022-04-06
Extending Censi's categorical co-design framework to dynamical systems.
2022 Workshop on Polynomial Functors
2022-03-29
Summary of the 2022 polynomial functors workshop.
Creating mathematics
2022-03-25
On whether doing mathematics is a creative act.
Poly makes me happy and smart
2022-01-19
A lighter, less technical tour of why Poly is delightful.
Creating new categories from old: Selection categories
2021-12-30
Building new categories from old, reminiscent of natural selection.
Deep neural networks as nested dynamical systems (with Tim Hosgood)
2021-11-05
Neural networks and dynamical systems as deeply interactive learning systems.
Poly inside Poly
2021-09-22
Using Awodey universes to represent polynomials inside Poly.
Dirichlet polynomials and entropy (with Tim Hosgood)
2021-07-25
Recovering Shannon entropy from Dirichlet polynomials and Huffman coding.
Jump monads: from conjugation to dependent types
2021-07-01
Relating dependent type theory to polynomials via universe polynomials.