17 citations · 30 across the 21 of their papers we have counts for
6 papers · 1 filter
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…
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…
A co-reflection of cubical sets into simplicial sets with applications to model structures
Chris Kapulkin, Zachery Lindsey, Liang Ze Wong
We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straighte…
Internal Languages of Finitely Complete -categories
Chris Kapulkin, Karol Szumiło
We prove that the homotopy theory of Joyal's tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-Löf…