3 papers
math.CT2025
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…
math.KT2025
Additivity and Fiber Sequences for Combinatorial K-Theory
Maru Sarazola, Brandon T. Shapiro
The (A)CGW categories of Campbell and Zakharevich show how finite sets and varieties behave like the objects of an exact category for the purpose of algebraic -theory. These str…
math.CT2025
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…