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Algebraically coherent categories: definition, examples and basic properties

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If you have a question about this talk, please contact Dr Ignacio Lopez Franco.

(Joint work with Alan S. Cigoli and James R. A. Gray) In a recent article, we call a regular category \emph{algebraically coherent} when the change-of-base functors in its fibration of points are \emph{coherent}, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. The present talk is an introduction to the concept of algebraic coherence, focusing on examples and basic properties. In particular, we will discuss equivalent conditions in the context of semi-abelian categories, as well as some consequences: amongst others, strong protomodularity, and normality of Higgins commutators of normal subobjects.

This talk is part of the Category Theory Seminar series.

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