From the 1 of 5 linked papers with an AI index.
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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…
Exponentiable Virtual Double Categories and Representability of Exponentials
Kevin D. Carlson, Ea E Thompson
Virtual double categories provide an effective framework for formal category theory. Recent work has investigated the question of higher morphisms between virtual double categories…
Presheaves on lax double functors; or, Instances of models of double theories
Kevin Carlson, Evan Patterson
We introduce a notion of (co)presheaf on a lax double functor , which we generally call an instance. In the terminology of double-categorical logic, a lax double functor valued…
Comparing loose bimodules and double barrels using pseudo-models of enhanced sketches
Jason Brown, Kevin Carlson, Sophie Libkind +1
(Pseudo) double categories have two sorts of morphisms: tight ones which compose strictly, and loose ones which compose up to coherent isomorphism. In this paper, we consider bimod…