A class of exactness properties characterized via left Kan extensions

Jacqmin, Pierre-Alain
(2022) Journal of Pure and Applied Algebra — Vol. 226, n° 1, p. 106784 (2022)

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  • Jacqmin, Pierre-AlainUCLouvain
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Abstract
We consider a general class of exactness properties on a finitely complete category, all of which can be expressed as the condition that a certain morphism in a diagram is a strong epimorphism. For each such exactness property, we characterize finitely bicomplete categories having the property by restricting the condition to those diagrams built from only one object in the category via a left Kan extension. In the regular context, this generalizes the theory of approximate co-operations introduced by D. Bourn and Z. Janelidze. As an application, we deduce from this a characterization of (essentially) algebraic categories satisfying such a given exactness property. The pointed version of these exactness properties is also studied.
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Jacqmin, P.-A. (2022). A class of exactness properties characterized via left Kan extensions. Journal of Pure and Applied Algebra, 226(1), 106784. https://doi.org/10.1016/j.jpaa.2021.106784 (Original work published 2022)