Proto-exact categories of matroids, Hall algebras, and K-theory

摘要

This paper examines the category Mat(circle) of pointed matroids and strong maps from the point of view of Hall algebras. We show that Mat(circle) 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(circle)) of Mat(circle) via the Waldhausen construction, and show that it is non-trivial, by exhibiting injections