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