2019/09/22 by Rune Haugseng, Haugseng, Rune
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1909.10042
Using the description of enriched ∞-operads as associative algebras in symmetric sequences, we define algebras for enriched ∞-operads as certain modules in symmetric sequences. For V a symmetric monoidal model category and O a Σ-cofibrant operad in V for which the model structure on V can be lifted to one on O-algebras, we then prove that strict algebras in V are equivalent to ∞-categorical algebras in the symmetric monoidal ∞-category associated to V. We also show that for an ∞-operad O enriched in a suitable closed symmetric monoidal ∞-category V, we can equivalently describe O-algebras in V as morphisms of ∞-operads from O to a self-enrichment of V.