Coproducts in categories of q-matroids

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Abstract

q-Matroids form the q-analogue of classical matroids. In this paper we introduce various types of maps between q-matroids. These maps are not necessarily linear, but they map subspaces to subspaces and respect the q-matroid structure in certain ways. The various types of maps give rise to different categories of q-matroids. We show that only one of these categories possesses a coproduct. This is the category where the morphisms are linear weak maps, that is, the rank of the image of any subspace is not larger than the rank of the subspace itself. The coproduct in this category is the very recently introduced direct sum of q-matroids.

Original languageEnglish
Article number103733
JournalEuropean Journal of Combinatorics
Volume112
DOIs
StatePublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Ltd

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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