ON INFINITE MATROIDS WITH STRONG MAPS: PROTO-EXACTNESS AND FINITENESS CONDITIONS

This paper investigates infinite matroids from a categorical perspective. We prove that the category of infinite matroids is a proto-exact category in the sense of Dyckerhoff and Kapranov, thereby generalizing our previous result on the category of finite matroids. We characterize finitary matroids as co-limits of finite matroids and show that the finitely presentable objects in this category are the finite matroids.