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Partial Mal'tsevness and partial protomodularity

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arxiv 1507.02886 v1 pith:2HLUH62Z submitted 2015-07-10 math.CT

Dominique Bourn This is my paper · ORCID
classification math.CT
keywords partialnotioncontextintroduceprotomodularitytsevtsevnessallows
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abstract

We introduce the notion of Mal'tsev reflection which allows us to set up a partial notion of Mal'tsevness with respect to a class $\Sigma$ of split epimorphisms stable under pullback and containing the isomorphisms, and we investigate what is remaining of the properties of the global Mal'tsev context. We introduce also the notion of partial protomodularity in the non-pointed context.

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  1. A direction functor approach to the cohomology of small categories

    math.CT 2026-08 conditional novelty 6.0 of 10

    For small categories over a fixed object set, cohomology can be computed via direction functors on S-special morphisms, matching Hoff and Golasinski cohomology in every degree.

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