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added looping/delooping statements to model structure on simplicial groupoids and model structure on presheaves of simplicial groupoids.
Question: Suppose we take the catgeory of genuine simplicial groupoids (no restriction on the simplicial set of objects). Does send degreewise fibrations to fibrations?
fixed glitches in text and references and added cross-link with model structure on simplicial groupoids
Re #4: it’s a general fact that if is a finitely complete cartesian closed category, then the same is true for the category of internal categories in . Same goes for . I have a proof sitting on my nLab page, which I can tidy up and create a page for on nLab main. (Oh, #4 is referring to the enriched case, not internal. Well, I’ll see about working that in as well.)
I still wanted to enhance the statement to make explicit the cartesian *enriched* monoidal structure. (Generally, the notion of enriched monoidal category seems to have been neglected by the classical authors. Of course here in the cartesian case it is not a big deal, but still.)
added pointer to:
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