Poset fiber theorems

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On sequentially Cohen-Macaulay complexes and posets (2007, background): “We also discuss a nonpure version of Quillen’s concept [15] of homotopy Cohen-Macaulayness, introduced by the authors in [6].”
Algebraic Topology of Finite Topological Spaces and Applications (2011, background): “In Quillen’s paper [70] and in many other articles ([17, 18, 79, 80] for instance), posets are studied from a topological viewpoint only through their associated simplicial complexes.”
Simple homotopy types and finite spaces (2006, background): “Finite spaces are closely related to finite posets, which have become an important tool in algebraic and geometric topology (see for example Quillen’s paper [12], Björner’s paper [3] and Björner, Wachs and Welker’s [4]).”