Non-free cocompletions

[Andree Ehresmann <andree.ehresmann@u-picardie.fr>]

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





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