5 papers · 1 filter
Homotopy -types of cubical sets and graphs
Chris Kapulkin, Udit Mavinkurve
We give a new construction of the model structure on the category of simplicial sets for homotopy -types, originally due to Elvira-Donazar and Hernandez-Paricio, using a right t…
Closed symmetric monoidal structures on the category of graphs
Chris Kapulkin, Nathan Kershaw
We show that the category of (reflexive) graphs and graph maps carries exactly two closed symmetric monoidal products: the box product and the categorical product.
A Toolkit for Structured Lifts
Chris Kapulkin, Yufeng Li
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply thes…
Pushforwards in Inverse Homotopical Diagrams
Chris Kapulkin, Yufeng Li
We establish a sufficient condition for the category of homotopical inverse diagrams to be closed under pushforward inside the category of inverse diagrams in a fibration category.
Logical Structure on Inverse Functor Categories
Marcelo Fiore, Chris Kapulkin, Yufeng Li
Inspired by recent work on the categorical semantics of dependent type theories, we investigate the following question: When is logical structure (crucially, dependent-product and…