# Extending homotopy theories across adjunctions

@article{Gurski2015ExtendingHT, title={Extending homotopy theories across adjunctions}, author={Nick Gurski and Niles Johnson and Ang'elica M. Osorno}, journal={arXiv: Algebraic Topology}, year={2015} }

Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can transport the weak equivalences from one category to another with the same objects and a broader class of maps. Under mild hypotheses this process produces an equivalence of homotopy theories. We describe examples including algebras over an operad, such as…

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