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added to complete Segal space a discussion of what an ordinary category looks like when regarded as a complete Segal space.
(This is meant to be pedagogical, therefore the recollection of all the basics at the beginning.)
added to the References at complete Segal space pointers to Bergner’s groupoidal version.
Added a remark that they are also called Rezk categories (at least by Joyal).
Thanks! Could you please cross-link that with Segal condition? There the Segal maps appear all over the place.
I did briefly cross-link now (also slightly edited your intro sentence at Segal map, please check).
There might be more cross-linking suitable to internal category in an (infinity,1)-category and maybe also at nerve.
I also like calling them “Rezk categories”. It has the double advantage of crediting Charles and indicating in the terminology that they are a kind of category.
Ah sorry, I hadn’t seen Segal condition.
@adeelkh: No problem, it’s good to have an entry Segal map as you created. But let’s make sure it’s cross-linked properly
@Mike: yes, we should further push that (change of) convention on the nLab, maybe it gets to stick
What do we call Segal spaces, in that case?
Rezk precategories.
The question keeps circulating whether the Rezk-complete Segal space canonically obtained from a relative category is equivalent as an $\infty$-category to the classical simplicial localization.
The $n$Lab entry complete Segal space had a link to the relevant MO discussion hidden somewhere. But since I was asked about this again now I have made the statement more explicit in a new section
The $n$Lab would be the ideal place to record not just the statement but also the proof in a stable way (adapting from what Chris Schommer-Pries and Denis-Charles Cisinki once said on MO, and maybe from published material which has appared since??). But I don’t have time to edit further now.
cross-linked with the new entry Rezk completion
added publication data for
and hyperlinked the references to this item
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