A detailed look at the Szczarba map

Emilio Minichiello; Mahmoud Zeinalian; Manuel Rivera

A detailed look at the Szczarba map

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arxiv 2305.13638 v1 pith:MI7FND7N submitted 2023-05-23 math.AT math.CT

Emilio Minichiello , Manuel Rivera , Mahmoud Zeinalian This is my paper · ORCID

classification math.ATmath.CT

keywords formulamodelsszczarbaadjointsarticlecategoricalchainclassifying

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We explain how to derive an explicit formula for a natural transformation relating the (left adjoints of) the homotopy coherent nerve and the Dwyer-Kan simplicial classifying space functor. The formula is derived using a method introduced by Szczarba when comparing two different chain models of a fibration. This note may be taken as a companion to section 3 of our previous article "Categorical models for path spaces".

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