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arXiv · 2607.25740

Lax Distributivity and a Characterization of Abelian Categories

Martin Markl·Dominik Trnka
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Abstract

We show that abelian categories can be characterized as structures consisting of a colax algebra and a lax algebra connected by a lax mixed rewriting rule. To this end we develop a theory of lax rewriting rules for pairs of lax-lax and colax-lax algebras over 2-monads.

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Martin Markl, Dominik Trnka. 2026-07-28. Lax Distributivity and a Characterization of Abelian Categories. https://arxiv.org/abs/2607.25740

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