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We use a classical result of McCord and reduction methods of finite spaces toprove a generalization of Thomason's theorem on homotopy colimits over posets.In particular this allows us to characterize the homotopy colimits of diagramsof simplicial complexes in terms of the Grothendieck construction on thediagrams of their face posets. We also derive analogues of well known resultson homotopy colimits in the combinatorial setting, including a cofinalitytheorem and a generalization of Quillen's Theorem A for posets.

Homotopy colimits of diagrams over posets and variations on a theorem of Thomason