On homotopy types modelized by strict \infty-groupoids
Algebraic Topology
2020-09-07 v2 Category Theory
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.
Cite
@article{arxiv.1206.2945,
title = {On homotopy types modelized by strict \infty-groupoids},
author = {Dimitri Ara},
journal= {arXiv preprint arXiv:1206.2945},
year = {2020}
}
Comments
22 pages, in French, v2: Conjecture 7.2 became Question 7.2, references added