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.
Homology, Homotopy and Applications, Vol. 4(2002), No. 1, pp. 59-69