2018/05/06 by Eppolito, Christopher, Jun, Jaiung, Szczesny, Matt · 1 citation
#05B35 #16T30 #18D99 (primary) #19A99 #19D99 (secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1805.02281
This paper examines the category Mat\bullet of pointed matroids and strong maps from the point of view of Hall algebras. We show that Mat\bullet has the structure of a finitary proto-exact category - a non-additive generalization of exact category due to Dyckerhoff-Kapranov. We define the algebraic K-theory K_* (Mat\bullet) of Mat\bullet via the Waldhausen construction, and show that it is non-trivial, by exhibiting injections πsn (\mathbbS) \hookrightarrow Kn (Mat\bullet) from the stable homotopy groups of spheres for all n. Finally, we show that the Hall algebra of Mat\bullet is a Hopf algebra dual to Schmitt's matroid-minor Hopf algebra.