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arXiv · 1705.03863

Gabriel-Morita theory for excisive model categories

Clemens Berger·Kruna Ratkovic
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Abstract

We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case.

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Clemens Berger, Kruna Ratkovic. 2017-05-10. Gabriel-Morita theory for excisive model categories. https://arxiv.org/abs/1705.03863

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