# Semicosimplicial totalization

Can somebody help me with a reference showing that the homotopy semicosimplicial totalization of a cosimplicial space is homotopy equivalent to its usual homotopy totalization? Is it because the inclusion of the semisimplicial category into the simplicial category is a homotopy left cofinal functor?

-
Having thought a little bit I proved that the inclusion of the semisimplicial category to the simplicial category is a homotopy left cofinal functor. But it must be a very standard thing and written somewhere. Can somebody help me with a reference? –  Victor Oct 15 '10 at 19:37