2017
DOI: 10.4310/hha.2017.v19.n2.a6
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Extending homotopy theories across adjunctions

Abstract: ABSTRACT. 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 symmetric mono… Show more

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Cited by 22 publications
(3 citation statements)
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“…Thomason [Tho95, 1.9.2] shows that each of the standard variants have equivalent stable homotopy theories. See [GJO17a] for a general treatment via 2-dimensional monad theory.…”
Section: Permutative Categoriesmentioning
confidence: 99%
“…Thomason [Tho95, 1.9.2] shows that each of the standard variants have equivalent stable homotopy theories. See [GJO17a] for a general treatment via 2-dimensional monad theory.…”
Section: Permutative Categoriesmentioning
confidence: 99%
“…Subsequent work of [BKP89, Her01, Lac02a, LP08], among many others, clarifies and extends this theory. Another approach using algebraic weak factorization systems is given in [BG16a,BG16b] and was further generalized to coherence theorems for strict and lax weak equivalences in [GJO17]. ◇ CHAPTER 7…”
Section: (Additional Features Of 2-monad Theorymentioning
confidence: 99%
“…50. In subsequent work[GJO17], the authors develop more general techniques and improve Corollaries 4.47 and 4.49 to equivalences of homotopy theories.…”
mentioning
confidence: 99%