On homotopy types modelized by strict \infty-groupoids

Dimitri Ara

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arXiv · 1206.2945

On homotopy types modelized by strict \infty-groupoids

Dimitri Ara

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Abstract

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 \infty-groupoids is equivalent to the derived category in homological degree greater or equal to 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.

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BibTeX RIS

Dimitri Ara. 2012-06-13. On homotopy types modelized by strict \infty-groupoids. https://arxiv.org/abs/1206.2945

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