20 papers
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…
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…
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…
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.
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…
Cofibration category of digraphs for path homology
Daniel Carranza, Brandon Doherty, Chris Kapulkin +3
We prove that the category of directed graphs and graph maps carries a cofibration category structure in which the weak equivalences are the graph maps inducing isomorphisms on pat…