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Someone deleted the contents of the entry simplicial localization on th 4 April, then another reinstated it on the 5th. Curious!
I added in the definition of “standard” simplicial localisation.
@ZhenLin: thanks! Great.
I have added some hyperlinks.
(I thought we did have an entry “relative category”, but apparently we don’t. But I think somewhere on the nLab these are discussed a little. Can’t search right now, as I have to run.)
You are invited to try your hand on something. Hit “edit” at the bottom of the page to edit the source.
added pointer to:
Changed the proposition directly under “### Simplicial localization of model categories”: the equivalence of (∞,1)-categories between the (bifibrant subcategory of) a simplicial model category and its simplicial localization at the weak equivalences only works if you let the former be a sSet-category, not a Set-category. This is also what Dwyer-Kan have in their paper, see property (iv) on their first page.
Arthur Pander Maat
cross-linked with complete Segal spaces#RelationToSimplicialLocalization.
Kensuke Arakawa
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