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.
Keywords: Proto-exact category, infinite matroids, finitary matroids
2020 MSC: 18D99, 05B35
Theory and Applications of Categories, Vol. 38, 2022, No. 11, pp 319-327.