Geodesic
Sur les types d'homotopie modélisés par les $\infty$-groupoides stricts
Theory and applications of categories, Tome 28 (2013), pp. 552-576

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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},
     publisher = {mathdoc},
     volume = {28},
     year = {2013},
     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/