Homology, Homotopy and Applications

Volume 4 (2002)

Number 1

A higher dimensional homotopy sequence

Pages: 59 – 69

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n1.a5

Authors

M. Grandis (Dipartimento di Matematica, Università di Genova, Italy)

E. M. Vitale (Département de Mathématique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

We associate to a continuous map between pointed spaces a long 2-exact sequence of homotopy pointed groupoids. The usual homotopy sequence of a map follows from this 2-exact sequence taking, for each groupoid, the set of connected components. We also study a condition of strong 2-exactness for a sequence of cat-groups and pointed groupoids.

Keywords

homotopical algebra, fundamental groupoids, homotopy sequences

2010 Mathematics Subject Classification

18G55, 20L05, 55Q05

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