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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…
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…
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…
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…