Date: Thu, 20 Oct 94 21:45:50 PDT From: john baez <baez@ucrmath.UCR.EDU>
I'm interested in colimits in the category of Hilbert spaces with isometries as morphisms. Is there a good reference on when these exist?
John Baez
I don't know a reference, but I know that very few colimits exist. For example, the sum of two non-zero spaces cannot exist for you can give the direct sum of the normed spaces either the sup or euclidean norm and these would both have to embed isometrically in the sum, which is clearly impossible. Clearly coequalizers are likewise precluded. It seems possible that filtered colimits might make it; you would take the ordinary colimit as inner product spaces and complete. I don't offhand see what can go wrong with that. Michael