We establish a Quillen equivalence between the homotopy theories of equivariant Segal operads and simplicial with norm maps. Together previous work, we further conclude that coherent nerve is right-Quillen from model category maps to structure for equivariant-$\infty$-operads in dendroidal sets.

We give conditions on a monoidal model category M and on a set of maps S so that the Bousfield localization of M with respect to S preserves the structure of algebras over various operads. This problem was motivated by an example due to Mike Hill which demonstrates that for the model category of equivariant spectra, even very nice localizations can fail to preserve commutativity. As a special c...

Abstract We construct a generalization of the Day convolution tensor product presheaves that works for certain double $$\infty $$ ∞ -categories. Using this construction, we obtain an -categorical version well-known description (one-object) operads as associative algebras in symmetric sequences; more generally...

Pairs of graded graphs, together with the Fomin property graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is one Young integer partitions, allowing us to connect number standard tableaux and numbers permutations. Here, we use operads, that algebraic devices abstracting notion composition objects, build pairs graphs. For...