Cohomology of Homotopy Colimits of Simplicial Sets and Small Categories

Fibrations and Homotopy Colimits of Simplicial Sheaves

We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the no...

Homotopy colimits in model categories

Colimits for the pro Category of Towers of Simplicial Sets

We describe a certain category of Ind-towers into which the Pro category of towers of simplicial sets embeds, and in which all colimits (rather than just the finite ones) may be constructed explicitly.

Homotopy (limits And) Colimits

These notes were written to accompany two talks given in the Algebraic Topology and Category Theory Proseminar at the University of Chicago in Winter 2009. When a category has some notion of limits and colimits associated to it, its ordinary limits and colimits are not necessarily homotopically meaningful. We describe a notion of a “homotopy colimit” for two sorts of categories with a homotopy ...

A Primer on Homotopy Colimits