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arXiv · 1512.01390

The category of matroids

Chris Heunen·Vaia Patta
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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; 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.

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Chris Heunen, Vaia Patta. 2018-09-23. The category of matroids. https://doi.org/10.1007/s10485-017-9490-2

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