On Infinite Matroids with Strong Maps: Proto-Exactness and Finiteness Conditions

Chris Eppolito and Jaiung Jun

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.

Published 2022-02-22.


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