4 papers
Comonads as spaces
Aaron David Fairbanks, Kevin Carlson, David I. Spivak
Comonads on Set generalize both categories and topological spaces. Expanding upon Garner's work on ionads, we develop aspects of the theory of topological spaces for arbitrary como…
Monads in 2-categories
Aaron David Fairbanks
This is a condensed overview of the formal theory of monads in a 2-category. Commutative diagrams and string diagrams are given side by side. In the string diagrams, each concept i…
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…