Vaughan Pratt writes
Incidentally, of what use are non-free cocompletions? Is there any reason not to define "cocompletion" to make it free?
I can indicate two important uses of non-free cocompletions, and more precisely cocompletions for particular classes of diagrams preserving some given colimits: 1. The construction of what, with Charles, we called the "prototype" and the "type" associated to a sketch (in "Categories of sketchd structures", Cahiers Top. et Geom. Diff. III-2, 1972) 2. The "complexification process" which, with Jean-Paul Vanbremeersch, we use extensively in our model for hierarchical evolutionary systems ("Memory Evolutive Systems: Hierarchy, Emergence, Cognition", Elsevier 2007) Kindly Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ]