Toward a Galoisian interpretation of homotopy theory
Algebraic Topology
2007-05-23 v4 Algebraic Geometry
Category Theory
Abstract
Given any pointed CW complex (X,x), it is well known that the fondamental group of X pointed at x is naturally isomorphic to the automorphism group of the functor which associates to a locally constant sheaf on X its fibre at x. The purpose of this work is to generalize this fact to higher homotopy. For this we introduce the (infinite) category of locally constant stacks on X, and we prove that the loop-space of endomorphisms of its fibre functor at x is naturally equivalent to the loop space of X based at x.
Keywords
Cite
@article{arxiv.math/0007157,
title = {Toward a Galoisian interpretation of homotopy theory},
author = {B. Toen},
journal= {arXiv preprint arXiv:math/0007157},
year = {2007}
}
Comments
French, 38 pages. To appear in "Cahiers de topologie et geometrie differentielle categoriques"