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.
A taxonomy of categories for relations
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abstract
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these ``categories for relations'', including their enriched version, further showing how they arise as Kleisli categories of symmetric monoidal monads. The resulting taxonomy aims at bringing clarity and organisation to the many related concepts and frameworks occurring in the literature.
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math.CT 1years
2025 1verdicts
ACCEPT 1representative citing papers
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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.