Homology, Homotopy and Applications

La catégorie cubique avec connexions est une catégorie test stricte

Georges Maltsiniotis

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The aim of this paper is to prove that the category of cubes with connections, introduced by R. Brown and Ph.J. Higgins, is a strict test category in Grothendieck's sense. In particular this implies that cubical sets with connections are models for homotopy types in a very precise sense, in a way that is compatible with the cartesian product.

Article information

Homology Homotopy Appl., Volume 11, Number 2 (2009), 309-326.

First available in Project Euclid: 27 January 2011

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Zentralblatt MATH identifier

Primary: 18G55: Homotopical algebra 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 18E35: Localization of categories 55P15: Classification of homotopy type 55U05: Abstract complexes

Catégorie test connexion ensemble cubique homotopie


Maltsiniotis, Georges. La catégorie cubique avec connexions est une catégorie test stricte. Homology Homotopy Appl. 11 (2009), no. 2, 309--326. https://projecteuclid.org/euclid.hha/1296138523

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