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08 February 2025
 
  » arxiv » 1508.0054

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Extending homotopy theories from strict maps to lax maps
Nick Gurski ; Niles Johnson ; Angélica M. Osorno ;
Date 1 Aug 2015
AbstractConstructions of spaces from symmetric monoidal categories or $Gamma$-categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal or lax natural. We describe conditions under which one can transport the weak equivalences from such a category of structured objects and strict maps to the corresponding category with the same objects and lax maps. Under mild hypotheses this process produces an equivalence of homotopy theories. We describe examples including algebras over an operad, such as symmetric monoidal categories and $n$-fold monoidal categories; and diagram categories, such as $Gamma$-categories.
Source arXiv, 1508.0054
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