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Rigid Matroid Categories

arxiv(2024)

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Abstract
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples include: deletion and contraction, 2-sum, series and parallel connections, the Tutte polynomial, gammoids, positroids, matroids representable over an infinite field, M-convex sets, and matroids associated to stable polynomials.
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