You can see here : agrothendieck.github.io

You can see here : agrothendieck.github.io

Here is the version 1: mathoverflow.net/questions/6551/…

You can also see here agrothendieck.github.io

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. . . )

This seems to be supported by Grothendieck himself. In a note of "Pursuing stacks" section 16bis pg 52, he says