Applied Categorical Structures

, Volume 27, Issue 1, pp 23–54 | Cite as

Gabriel-Morita Theory for Excisive Model Categories

  • Clemens Berger
  • Kruna RatkovicEmail author


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.


Homotopical algebra Strong monad Excision Bar resolution 

Mathematics Subject Classification

Primary 18G55 18C15 Secondary 18D25 55P42 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Lab. J. A. DieudonnéUniversité de NiceParc Valrose, Nice CedexFrance
  2. 2.Faculty of Applied SciencesUniversity of Donja GoricaDonja Gorica, PodgoricaMontenegro

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