From the 2 of 4 linked papers with an AI index.
4 papers
Comonads as spaces
Aaron David Fairbanks, Kevin Carlson, David I. Spivak
The paper develops a theory linking comonads on Set to topological spaces, introducing density comonads as abstract subbases and showing how every comonad yields an underlying spac…
Monads in 2-categories
Aaron David Fairbanks
The paper provides a concise overview of the formal theory of monads within 2‑categories, illustrating concepts with both commutative and string diagrams and introducing related st…
Doubly weak double categories
Aaron David Fairbanks, Michael Shulman
We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad -- a structure with…
On Traces in Categories of Contractions
Aaron David Fairbanks, Peter Selinger
Traced monoidal categories are used to model processes that can feed their outputs back to their own inputs, abstracting iteration. The category of finite dimensional Hilbert space…