2017/05/10 by Clemens Berger, Berger, Clemens, Kruna Ratković +1
Computer Science · Mathematics · #18C15 (Primary) #18D25 #18G55 #55P42 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1705.03863
openalex publication_date 2017/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.