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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 26th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Idea A refinement of the notion of [[homotopy category]] of a [[model category]] (more generally, [[relative category]]) that keeps track of homotopies between morphisms. Dwyer–Kan implement the notion of a simplicial homotopy category as a simplicial category that is Dwyer–Kan equivalent to the [[hammock localization]]. ## Related concepts * [[homotopy category]] * [[category of fractions]] * [[hammock localization]] ## References See §5.1 in * {#DwyerKan80FunctionComplexes} [[William G. Dwyer]], [[Daniel M. Kan]], _Function complexes in homotopical algebra_, Topology 19 (1980), 427-440 &lbrack;<a href="https://doi.org/10.1016/0040-9383(80)90025-7">doi:10.1016/0040-9383(80)90025-7</a>, [pdf](https://people.math.rochester.edu/faculty/doug/otherpapers/dwyer-kan-3.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/simplicial+homotopy+category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/simplicial+homotopy+category">current</a>

   Created:

   Idea

   A refinement of the notion of homotopy category of a model category (more generally, relative category) that keeps track of homotopies between morphisms.

   Dwyer–Kan implement the notion of a simplicial homotopy category as a simplicial category that is Dwyer–Kan equivalent to the hammock localization.

   Related concepts

   • homotopy category

   • category of fractions

   • hammock localization

   References

   See §5.1 in

   • {#DwyerKan80FunctionComplexes} William G. Dwyer, Daniel M. Kan, Function complexes in homotopical algebra, Topology 19 (1980), 427-440 [doi:10.1016/0040-9383(80)90025-7, pdf]

   v1, current