Brown representability for directed graphs

2020/03/16 by McGuirk, Zachary, Park, Byungdo
#05C20 #55P99 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.07426

Abstract

We prove that any contravariant functor from the homotopy category of finite directed graphs to abelian groups satisfying the additivity axiom and the Mayer-Vietoris axiom is representable.

Related

• Brown functors of directed graphs
• Representability theorems, up to homotopy
• A representability theorem for some huge abelian categories
• Derived categories, resolutions, and Brown representability
• The dual of Brown representability for homotopy categories of complexes