Tensor-restriction categories

C. Heunen; J. S. Pacaud Lemay

Tensor-restriction categories

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arxiv 2009.12432 v4 pith:CV67Y2TQ submitted 2020-09-25 math.CT

C. Heunen , J. S. Pacaud Lemay This is my paper · ORCID

classification math.CT

keywords categoriesmonoidalrestrictioncategorydefinedmapspartiallyrespect

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Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are partially defined with respect to this spatial structure. We introduce a construction that turns a firm monoidal category into a restriction category and axiomatise the monoidal restriction categories that arise this way, called tensor-restriction categories.

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Partializations of Markov categories
math.CT 2025-09 accept novelty 7.0 of 10

Given a partializable Markov category C, the span-based category Partial(C) is a positive quasi-Markov CD category that inherits representability, conditionals, Kolmogorov products, and idempotent splittings.

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