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added this pointer:
added also pointer to
(who does finally switch terminology from “simplicial groupoid” to “groupoid enriched over simplicial sets” but still does not state the definition of enriched groupoids)
together with more comments on the history of the notion.
Presumably the assumption that be a cosmos can be relaxed to simply asking for to be a cartesian monoidal category?
how about formulating it this way:
…a cartesian monoidal category (serving as an cosmos for enrichment)…
I think varkor is suggesting that the cosmos (or cartesian cosmos) assumptions are rather more than what is needed. In that case, I wouldn’t say “cosmos for enrichment”, but “base for enrichment” or something similar. Not sure we have a page that accommodates that extra generality, but if not, I think we should.
I know, that’s why I suggested the reformulation “serving as…”.
Now base of enrichment is redirecting to cosmos. Feel invited to split it off as a separate entry.
Have to admit that I am not sure what you are getting at with either of these comments.
We need a cartesian monoidal base of enrichment in order to state the enriched existence of inverses. The entry is clear about this, and the notation seemed just fine.
Whether this encompasses “ordered groups” is something that the entry on ordered groups needs to deal with. The notion of enriched groupoids is what it is.
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