Post date: 01-oct-2015 17:24:54
In this talk we introduce the bar construction, from a suitable pair of functors F, G ( with G being a simplicial weight ) this construction produces a simplicial object, and then take a geometric realization ( this is a sort of "fattened up" colimit ) of this simplicial object, which in the next talk we will show that under natural hypothesis computes the homotopy colimit (when we take G to be constant at the final object).
We will make precise the meaning of "fattened up" colimit by the theory of weighted colimits and final functors, explicitly take G to be constant at the final object, then the colimit of the simplicial object is the colimit of F, while the geometric realization of the simplicial object is the weighted colimit of F by the nerve N(-/D).