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Article Dans Une Revue Applied Categorical Structures Année : 2019

Gabriel-Morita theory for excisive model categories

Résumé

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.

Dates et versions

hal-03613196 , version 1 (18-03-2022)

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Citer

Clemens Berger, Kruna Ratkovic. Gabriel-Morita theory for excisive model categories. Applied Categorical Structures, 2019. ⟨hal-03613196⟩
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