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math.CO2022
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…
math.AT2022
Cubical models of higher categories without connections
Brandon Doherty
We prove that each of the model structures for (-trivial, saturated) comical sets on the category of marked cubical sets having only faces and degeneracies (without connections)…