3 citations · 6 across the 8 of their papers we have counts for
8 papers
Extensional concepts in intensional type theory, revisited
Chris Kapulkin, Yufeng Li
Revisiting a classic result from M. Hofmann's dissertation, we give a direct proof of Morita equivalence, in the sense of V. Isaev, between extensional type theory and intensional…
Nonexistence of colimits in naive discrete homotopy theory
Daniel Carranza, Chris Kapulkin, Jinho Kim
We show that the quasicategory defined as the localization of the category of (simple) graphs at the class of A-homotopy equivalences does not admit colimits. In particular, we set…
The fundamental group in discrete homotopy theory
Chris Kapulkin, Udit Mavinkurve
We develop a robust foundation for studying the fundamental group(oid) in discrete homotopy theory, including: equivalent definitions and basic properties, the theory of covering g…
The Hurewicz theorem for cubical homology
Daniel Carranza, Chris Kapulkin, Andrew Tonks
We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical…
Cubical setting for discrete homotopy theory, revisited
Daniel Carranza, Chris Kapulkin
We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide wit…
Homotopy groups of cubical sets
Daniel Carranza, Chris Kapulkin
We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that the…
Equivalence of cubical and simplicial approaches to -categories
Brandon Doherty, Chris Kapulkin, Yuki Maehara
We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for (-trivial, saturated) comical sets to the category of…
A cubical model for -categories
Tim Campion, Chris Kapulkin, Yuki Maehara
We propose a new model for the theory of -categories (including the case ) in the category of marked cubical sets with connections, similar in flavor to compl…