17 citations · 30 across the 21 of their papers we have counts for
9 papers · 1 filter
Yet another cubical type theory, but via a semantic approach
Chris Kapulkin, Yufeng Li
We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to…
(Pointed) Univalence in Universe Category Models of Type Theory
Chris Kapulkin, Yufeng Li
We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further devel…
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…
Biclosed monoidal structures on the categories of digraphs and graphs
Adrien Grenier, Chris Kapulkin
We show that the categories of directed and undirected reflexive graphs carry exactly two (up to isomorphism) biclosed monoidal structures.
Cubical models of -presheaves and the Bousfield-Kan formula
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
We construct the covariant and the cocartesian model structures on the slice categories of cubical sets and marked cubical sets, respectively. As an application, we derive a versio…
Derived mapping spaces of -categories
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for -categories, and allows us to provide a unif…
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.
Topological data analysis using persistent discrete homology
Chris Kapulkin, Nathan Kershaw
We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods. In particular, we provide empirical evidence t…
Categorical foundations of discrete dynamical systems
Daniel Carranza, Chris Kapulkin, Nathan Kershaw +2
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. We introduce the notion of cycle sets…