Homotopy colimit of spaces
= Homotopy colimit of spaces
= Homotopy colimits of spaces
{synonym}
A <homotopy colimit of spaces> is the homotopy-invariant replacement for a <colimit> of spaces. For a filtered diagram of <CW complexes> with subcomplex inclusions, the union is a model: the inclusions are <cofibrations>, and every sphere map and homotopy has image in a finite subcomplex. A <suspension spectrum> carries this construction to the corresponding <homotopy colimit of spectra>.