2023/06/04 by Carranza, Daniel, Kapulkin, Chris, Kim, Jinho · 1 citation
#05C25 (primary) #18N50 (secondary) #18N60 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.02219
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 settle in the negative the question of whether the A-homotopy equivalences in the category of graphs are part of a model structure.