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arXiv · 2608.07380

A direction functor approach to the cohomology of small categories

Stefano Ambra·Arnaud Duvieusart·Andrea Montoli
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Abstract

We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixed section. Using the fact that, for any set B, the category of small categories with B as set of object is S-Maltsev with respect to the class of Schreier points, we show that the cohomology theory of small categories arising from the direction functors coincides with the one introduced by Hoff and Golasinski.

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Stefano Ambra, Arnaud Duvieusart, Andrea Montoli. 2026-08-07. A direction functor approach to the cohomology of small categories. https://arxiv.org/abs/2608.07380

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