Dear category theorists, Sorry for my following stupid questions , but i would like: -Given a monoidal category M , for first assumed to be strict, What kind of thing do we obtain when we take it's classifying space ?: we take the nerve of M and then realising the simplicial sets obtained Explicitely there are theses questions : 1) Does the nerve of M "preserve" (or "reflect") the monoidal structure of M ? -Is it a monoid in the category of simplicial sets ? -If yes , can we have conditions on a monoid of sSet to be the nerve of a monoidal category ? I mean, does some kind of "segal condition" ? 2) And What kind of topological spaces of the realization of the nerve -Is it a topological monoid , with some extra structure ? 3) And what hapen if M is not strict, or is symmetric, or braided , etc... Thank you and sorry if these are completely stupid questions