Brandon Doherty: A cofibration category of directed graphs

Abstract

Cofibration categories are categories equipped with designated classes of morphisms, called cofibrations and weak equivalences, satisfying certain properties which allow for the convenient construction of a homotopy category. Similar in concept to model categories, though weaker, cofibration categories (suitably defined) present homotopy theories having all small homotopy colimits. In this talk, based on ongoing joint work with Carranza, Kapulkin, Opie, Sarazola, and Wong, I will describe a new cofibration category structure on the category of directed graphs, whose weak equivalences are maps inducing isomorphisms on the path homology groups defined by Grigor’yan, Lin, Muranov, and Yau.