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- Title
Proto-exact categories of matroids, Hall algebras, and K-theory.
- Authors
Eppolito, Chris; Jun, Jaiung; Szczesny, Matt
- Abstract
This paper examines the category Mat ∙ of pointed matroids and strong maps from the point of view of Hall algebras. We show that Mat ∙ 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 ∙) of Mat ∙ via the Waldhausen construction, and show that it is non-trivial, by exhibiting injections π n s (S) ↪ K n (Mat ∙) from the stable homotopy groups of spheres for all n. Finally, we show that the Hall algebra of Mat ∙ is a Hopf algebra dual to Schmitt's matroid-minor Hopf algebra.
- Publication
Mathematische Zeitschrift, 2020, Vol 296, Issue 1/2, p147
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-019-02429-z