(1) What are some good references for homotopy colimits?


(2) Where can I find a reference for the following concrete construction of a homotopy colimit? Start with a partial ordering, which I will think of as a category and also as a directed graph (objects = vertices, morphisms = edges). Assume we have a functor $F$ from the graph into (say) chain complexes. We will construct a big chain complex (the homotopy colimit) in stages.


Stage 0: direct sum over all vertices $v$ of $F(v)$


Stage 1: direct sum over all edges $e$ of the mapping cylinder of $F(e)$, with the ends of the mapping cylinder identified with the appropriate parts of stage 0.


Stage 2: direct sum over all pairs of composable edges $(e\_1, e\_2)$ of a higher order mapping cylinder, with appropriate identifications to parts of stage 1. This implements a relation between the three stage 1 mapping cylinders corresponding to $e\_1, e\_2$ and $e\_1\*e\_2$.


Stage 3: direct sum over all triples of composable edges $(e\_1, e\_2, e\_3) \dots$



References for homotopy colimit
I'm way late on this one, but for the record I'll point out that a nice answer to question 2 can be found in Hatcher's Algebraic Topology book, Section 4.G.


