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

TL;DR

This paper explores the categorical structure of infinite matroids, establishing that they form a proto-exact category, and characterizes finitary matroids as co-limits of finite matroids, extending previous finite matroid results.

Contribution

It proves that the category of infinite matroids is proto-exact and characterizes finitary matroids as co-limits of finite matroids, generalizing finite matroid theory.

Findings

Category of infinite matroids is proto-exact

Finitary matroids are co-limits of finite matroids

Finite matroids are finitely presentable objects

Abstract

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 also characterize finitary matroids as co-limits of finite matroids, and show that the finite matroids are precisely the finitely presentable objects in this category.