Homotopy limit

Summary

A homotopy limit is the version of a limit that respects weak equivalences. Ordinary limits of diagrams of spaces can change drastically when the diagram is replaced by a weakly equivalent one; homotopy limits do not. In a model category the homotopy limit is the right derived functor of the limit functor. Homotopy pullbacks, homotopy fixed points and the space of maps out of a homotopy colimit are typical instances.