In a paper by M.Kelly `A unified treatment of transfinite construction for free algebras, free monoids, colimits, associated sheaves, and so on', Bull. of the Australian Math. Soc., 22 (1980), 1-85. there is a general construction of colimits in the category of algebras of a finitary monad. The category of 1-Cat is an algebra of a free category on graph monad, which is finatary so the colimits exist in 1-Cat. Informally what we have to do to construct a coequalizer in 1-Cat is the following. First we have to construct a corresponding coequalizer in graphs. Then apply free category functor to it and form another coequaliser in graphs. This process continuing. Finally we have a sequence of graphs and its colimit is our coequalizer in 1-Cat. The same argument show the existence of colimits in n-Cat (strict n-categories and strict n-functor) or weak n-Cat with strict n-functors (if you accept my definition of weak n-catgory introduced in 'Monoidal globular categories as a natural environment for the theory of weak $n$-categories', Adv. Math. 136 (1998), pp. 39-103.). If we think of n-Cat as a category of algebras over an appropriate n-operad then it contains a full subcategory of algebras such that their underlying n-graphs (n-globular sets in other terminology) are discretes in dimension n (i.e. Hom(a,b) = 0 if a /ne b and Hom(a,a)=1). This subcategory is closed under limits and so we have a left adjoint from n-Cat to this subcategory which can be considered as a decategorification functor. Therefore, it commutes with colimits. Michael Batanin. 29-Jan-2002 20:56:51 -0400,1875;000000000000-00000000