Related papers: Segalification and the Boardman-Vogt tensor produc…

Some sufficient conditions on a simplicial space $X$ guaranteeing that $X_1\simeq \Omega|X|$ were given by Segal. We give a generalization of this result for multisimplicial spaces. This generalization is appropriate for the reduced bar…

We affirm and generalize a conjecture of Blumberg and Hill: unital weak $\mathcal{N}_\infty$-operads are closed under $\infty$-categorical Boardman-Vogt tensor products and the resulting tensor products correspond with joins of weak…

We introduce higher dimensional analogues of simplicial constructions due to Segal and Waldhausen, respectively producing the direct sum and algebraic $K$-theory spectra of an exact category. We then investigate their fibrancy properties,…

We discuss right fibrations in the $\infty$-categorical context of Segal objects in a category V and prove some basic results about these.

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on…

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We…

We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.

We establish a combinatorial model for the Boardman--Vogt tensor product of several absolutely free operads, that is free symmetric operads that are also free as $\mathbb{S}$-modules. Our results imply that such a tensor product is always a…

We introduce the wreath product for a class of operadic categories and use it to construct an explicit isomorphism between the Boardman-Vogt tensor product of two colored operads in Set and an operad induced by the wreath product of…

We introduce the analogues of the notions of complete Segal space and of Segal category in the context of equivariant operads with norm maps, and build model categories with these as the fibrant objects. We then show that these model…

It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such, flagged $(\infty,n)$-categories provide a model-independent formulation of Segal…

A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold, as a generalization of similar structures…

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of $n$-fold loop spaces is shown to be equivalent to the homotopy theory of reduced $\Theta_n$-spaces, where $\Theta_n$ is an iterated wreath product of the simplex…

This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…

For a given twisted cartesian products of simplicial sets, we construct the corresponding twisted tensor product in the sense of Brown, with an explicit twisting function whose formula is simple without using inductions. This is done by…

We give a new, construction-free proof of the associativity of tensor product for modules for rational vertex operator algebras under certain convergence conditions.