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.
Tensor-restriction categories
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abstract
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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math.CT 1years
2025 1verdicts
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Partializations of Markov categories
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.