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Pré-Publication, Document De Travail Année : 2020

HOMOLOGY OF CATEGORIES VIA POLYGRAPHIC RESOLUTIONS

Résumé

In this paper, we extend a result of Lafont and Métayer and prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category ωCat of strict ω-categories, is naturally isomorphic to the homology of its nerve. Along the way, we prove some results on homotopy colimits with respect to the Folk model structure and deduce a theorem which formally resembles Quillen's Theorem A.
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Dates et versions

hal-02512607 , version 1 (19-03-2020)
hal-02512607 , version 2 (23-03-2020)
hal-02512607 , version 3 (20-02-2021)

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  • HAL Id : hal-02512607 , version 1

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Léonard Guetta. HOMOLOGY OF CATEGORIES VIA POLYGRAPHIC RESOLUTIONS. 2020. ⟨hal-02512607v1⟩
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