arXiv subjects
Publications and source records attributed to David Jaz Myers.
Polynomial functors are sums of covariant representable functors from the category of sets to itself. They have a robust theory with many applications -- from operads and opetopes to combinatorial species. In this paper, we define a contravariant analogue of polynomial functors: Dirichlet functors. We develop the basic theory of Dirichlet functors, and relate them to their covariant analogues.
In this paper, we exhibit a "Yoneda"-style embedding of any virtual equipment into the virtual equipment of categories enriched in it. We show that this embedding preserves composition, is full on 2-cells and arrows, and coreflective on proarrows.
A popular graphical calculus for monoidal categories makes computations tactile and intuitive. Complicated diagram chases can be expressed in a few pictures and discovered by playing with a shoelace. Joyal and Street's proof of the soundness of this calculus says that any deformation of a diagram, any bending of the strings, describes the same morphism. In this paper, we extend the graphical calculus to double categories and proarrow equipments in order to bring the string diagrammatic method to formal category theory. Our main theorem proves this calculus sound with the help of Dawson and Pare's results on composition in double categories.