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Admissibility and rectification of colored symmetric operads

Research paper by Dmitri Pavlov, Jakob Scholbach

Indexed on: 29 Oct '15Published on: 29 Oct '15Published in: Mathematics - Algebraic Topology



Abstract

We establish a flexible condition that guarantees that all colored symmetric operads in a symmetric monoidal model category are admissible, i.e., the category of algebras over any operad admits a model structure transferred from the original model category. We also give a criterion that ensures that any weak equivalence of admissible operads admits rectification, i.e., the corresponding Quillen adjunction between the categories of algebras is a Quillen equivalence. In addition, we show that Quillen equivalences of underlying symmetric monoidal model categories yield Quillen equivalences of model categories of algebras over operads. Applications of these results include enriched categories, colored operads, prefactorization algebras, and commutative symmetric ring spectra.