Geodesic
Sur les types d'homotopie modélisés par les $\infty$-groupoides stricts
Theory and applications of categories, Tome 28 (2013), pp. 552-576 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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The purpose of this text is the study of the class of homotopy types which are modelized by strict $\infty$-groupoids. We show that the homotopy category of simply connected strict $\infty$-groupoids is equivalent to the derived category in homological degree $d \ge 2$ of abelian groups. We deduce that the simply connected homotopy types modelized by strict $\infty$-groupoids are precisely the products of Eilenberg-Mac Lane spaces. We also briefly study 3-categories with weak inverses. We finish by two questions about the problem suggested by the title of this text.

Publié le :
Classification : 18B40, 18D05, 18E30, 18E35, 18G35, 18G55, 55P10, 55P15, 55Q05, 55U15, 55U25, 55U35
Keywords: strict $\infty$-groupoid, homotopy type, chain complex, homotopy category, Eilenberg-Mac Lane space 
@article{TAC_2013_28_a18,
     author = {Dimitri Ara},
     title = {Sur les types d'homotopie mod\'elis\'es par les
$\infty$-groupoides stricts},
     journal = {Theory and applications of categories},
     pages = {552--576},
     year = {2013},
     volume = {28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2013_28_a18/}
}
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Dimitri Ara. Sur les types d'homotopie modélisés par les
$\infty$-groupoides stricts. Theory and applications of categories, Tome 28 (2013), pp. 552-576. http://geodesic.mathdoc.fr/item/TAC_2013_28_a18/