4 papers · 1 filter
Familial Monads as Higher Category Theories
Brandon Shapiro
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explici…
Duoidal Structures for Compositional Dependence
Brandon T. Shapiro, David I. Spivak
We provide a categorical framework for mathematical objects for which there is both a sort of "independent" and "dependent" composition. Namely we model them as duoidal categories…
All Concepts are
Owen Lynch, Brandon T. Shapiro, David I. Spivak
We show that the double category of comonoids in the category of polynomial functors (previously shown by Ahman-Uustalu and Garner to be equivalent to th…
A Polynomial Construction of Nerves for Higher Categories
Brandon T. Shapiro, David I. Spivak
We show that the construction due to Leinster and Weber of a generalized Lawvere theory for a familially representable monad on a (co)presheaf category, and the associated ``nerve'…