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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeSep 6th 2011

I’ve removed this query box from metric space and incorporated its information into the text:

Mike: Perhaps it would be more accurate to say that the symmetry axiom gives us enriched $\dagger$-categories?

Toby: Yeah, that could work. I was thinking of arguing that it makes sense to enrich groupoids in any monoidal poset, cartesian or otherwise, since we can write down the operations and all equations are trivial in a poset. But maybe it makes more sense to call those enriched $\dagger$-categories.