Homology, Homotopy and Applications
Volume 4 (2002)
A higher dimensional homotopy sequence
Pages: 59 – 69
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.
homotopical algebra, fundamental groupoids, homotopy sequences
2010 Mathematics Subject Classification
18G55, 20L05, 55Q05