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arXiv · 2609.29967

Groupoidal polygraphic homology

Léonard Guetta·François Métayer
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Abstract

We show that for a 1-category C, the (ω, k)-polygraphic homology of C for any k {\geq} 1, that is taken with cofibrant resolutions in strict (ω, k)- categories, does not depend on k and is canonically isomorphic to the homology of the classifying space of C. When C is a groupoid, we also show this for k = 0. In particular, this means that the classical homology of groups can be obtained by taking cofibrant resolutions in strict ω-groupoids. In order to show these results, we develop the theory of discrete Conduché fibrations in the category of strict (ω, k)-categories, building on previous work by the first-named author.

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Léonard Guetta, François Métayer. 2026-09-24. Groupoidal polygraphic homology. https://arxiv.org/abs/2609.29967

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