• Corpus ID: 245836919

Categorical models for path spaces

@inproceedings{Minichiello2022CategoricalMF,
  title={Categorical models for path spaces},
  author={Emilio Minichiello and Manuel Rivera and Mahmoud Zeinalian},
  year={2022}
}
We establish an explicit comparison between two constructions in homotopy theory: the left adjoint of the homotopy coherent nerve functor, also known as the rigidification functor, and the Kan loop groupoid functor. This is achieved by considering localizations of the rigidification functor, unraveling a construction of Hinich, and using a sequence of operators originally introduced by Szczarba in 1961. As a result, we obtain several combinatorial space-level models for the path category of a… 
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