Dear all, By inclusion of topological spaces, I mean a continuous map i:A-->X which is one-to-one and which induces an homeomorphism between A and i(A) equipped with the relative topology coming from X (in general, A may contain more open subspaces than i(A)). Take a topological 1-category X. Take two 1-subcategories A and B of X (the inclusion maps from A and B to X are inclusions in the above sense). One supposes that the canonical 1-functor from the colimit A \sqcup_{A\cap B} B to X is one-to-one (i.e. the underlying set map) so that if we forget the topology, A \sqcup_{A\cap B} B is isomorphic to the 1-subcategory of X generated by A and B. Is this 1-functor an inclusion of topological spaces (i.e. the underlying continuous map) ? pg. 13-May-2002 07:32:31 -0300,1777;000000000001-00000000