English

A detailed look at the Szczarba map

Algebraic Topology 2023-05-24 v1 Category Theory

Abstract

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".

Keywords

Cite

@article{arxiv.2305.13638,
  title  = {A detailed look at the Szczarba map},
  author = {Emilio Minichiello and Manuel Rivera and Mahmoud Zeinalian},
  journal= {arXiv preprint arXiv:2305.13638},
  year   = {2023}
}