2 papers
math.CT2026
Lax Distributivity and a Characterization of Abelian Categories
Martin Markl, Dominik Trnka
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…
math.CT2026
Kernels, lax algebras, décalage, and supercoherence
Martin Markl, Dominik Trnka
We prove that a pointed category has kernels if and only if it is a lax algebra for the arrow 2-monad, and that this holds if and only if it is the décalage of a supercoherent str…