The Category of Matroids

Christiaan Heunen, Vaia Patta

Research output: Contribution to journalArticlepeer-review

Abstract

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful and having a nearly full Kan extension; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial.
Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalApplied Categorical Structures
Early online date20 Apr 2017
DOIs
Publication statusE-pub ahead of print - 20 Apr 2017

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