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Dec 6, 2021 at 5:12 vote accept user234212323
Dec 6, 2021 at 3:48 comment added user234212323 The definition of the nerve functor, realizing a full embedding of (Cat) into \Simplexˆ, is given for the first time (I believe) in a Bourbaki talk of mine, which at that time wasn’t concerned at all with the topological interpretation of small categories, but with some rather formal prerequisites for the operation of “passage to quotient” of an object by a “pre-equivalence relation”, in any category (with a view of applying it in the category of schemes. . . )
Dec 6, 2021 at 3:48 comment added user234212323 This seems to be supported by Grothendieck himself. In a note of "Pursuing stacks" section 16bis pg 52, he says
S Dec 5, 2021 at 16:49 review First answers
Dec 5, 2021 at 17:12
S Dec 5, 2021 at 16:49 history answered Thomas Holder CC BY-SA 4.0