4 papers
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…
Equivalence of cubical and simplicial approaches to -categories
Brandon Doherty, Chris Kapulkin, Yuki Maehara
We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for (-trivial, saturated) comical sets to the category of…
Models for cyclic infinity operads
Brandon Doherty, Philip Hackney
We construct model structures on cyclic dendroidal sets and cyclic dendroidal spaces for cyclic quasi-operads and complete cyclic dendroidal Segal spaces, respectively. We show the…
Symmetry in the cubical Joyal model structure
Brandon Doherty
We study properties of the cubical Joyal model structures on cubical sets by means of a combinatorial construction which allows for convenient comparisons between categories of cub…