Diagonal fibrations are pointwise fibrations

Details Diagonal fibrations are pointwise fibrations Diagonal fibrations are pointwise fibrations

2007-06-28

arxiv.org/abs/0706.4279v1

Mathematics

Algebraic Topology

to be published in "Journal of Homotopy and Related Structures"

Scientific paper

On the category of bisimplicial sets there are different Quillen closed model structures associated to various definitions of fibrations. In one of them, which is due to Bousfield and Kan and that consists of seeing a bisimplicial set as a simplicial object in the category of simplicial sets, fibrations are those bisimplicial set maps such that each of the induced simplicial set maps is a Kan fibration, that is, the pointwise fibrations. In another of them, introduced by Moerdijk, a bisimplicial map is a fibration if it induces a Kan fibration of associated diagonal simplicial sets, that is, the diagonal fibrations. In this note, we prove that every diagonal fibration is a pointwise fibration.

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