8 papers · 1 filter
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…
Synthetic approach to the Quillen model structure on topological spaces
Sterling Ebel, Chris Kapulkin
We provide an axiomatic treatment of Quillen's construction of the model structure on topological spaces to make it applicable to a wider range of settings, including -generate…
Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories
Daniel Carranza, Chris Kapulkin, Liang Ze Wong
The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal…
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…
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…