3 citations · 5 across the 13 of their papers we have counts for
4 papers · 1 filter
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…
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…