Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

La catégorie cubique avec connexions est une catégorie test stricte

Pages: 309 – 326

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a15


Georges Maltsiniotis (Institut de Mathématiques de Jussieu, Université Paris 7 Denis Diderot, Paris, France)


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.


catégorie test; connexion; ensemble cubique; homotopie

2010 Mathematics Subject Classification

18D10, 18E35, 18G55, 55P15, 55U05

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Published 1 January 2009