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math.CO2025
Biclosed monoidal structures on the categories of digraphs and graphs
Adrien Grenier, Chris Kapulkin
We show that the categories of directed and undirected reflexive graphs carry exactly two (up to isomorphism) biclosed monoidal structures.
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…