Related papers: Segalification and the Boardman-Vogt tensor produc…
Dyckerhoff--Kapranov and G\'alvez-Carrillo--Kock--Tonks independently introduced the notion of a $2$-Segal space, that is, a simplicial space satisfying $2$-dimensional analogues of the Segal conditions, as a unifying framework for…
We prove that Sobolev spaces on Cartesian and warped products of metric spaces tensorize, only requiring that one of the factors is a doubling space supporting a Poincar\'e inequality.
This note explains how the two measures used to define the $\mu$-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves…
We give a new proof of the equivalence between two of the main models for $(\infty,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the $\Theta_{n}$-spaces of Rezk, by proving that these are algebras for the same monad on the…
We give an explicit description of the twisted arrow construction for simplicial spaces and demonstrate individually that it preserves the defining properties of a complete Segal space. Moreover, we show that for a Segal space, the natural…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
The notion of a higher Segal space was introduced by Dyckerhoff and Kapranov as a general framework for studying higher associativity inherent in a wide range of mathematical objects. In the present work we formalize the connection between…
A construction related to the Boardman-Vogt tensor product of operads allows us to describe the configuration category of a product manifold $M\times N$ in terms of the configuration categories of the factors $M$ and $N$.
We use the complete Segal approach to the theory of Cartesian fibrations to define and study representable Cartesian fibrations, generalizing representable right fibrations which have played a key role in $\infty$-category theory. In…
We develop an alternative to the May-Thomason construction used to compare operad based infinite loop machines to that of Segal, which relies on weak products. Our construction has the advantage that it can be carried out in $Cat$, whereas…
We introduce a relative version of the $2$-Segal simplicial spaces defined by Dyckerhoff and Kapranov and G\'{a}lvez-Carrillo, Kock and Tonks. Examples of relative $2$-Segal spaces include the categorified unoriented cyclic nerve, real…
We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…
The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory.…
We define complete Segal objects, which play the role of internal higher category objects. Then we study them using representable Cartesian fibrations, in particular defining adjunctions and limits of complete Segal objects. Finally we use…
We advance the foundational study of be Nardin-Shah's $\infty$-category of $G$-operads and their associated $\infty$-categories of algebras. In particular, we construct the underlying $G$-symmetric sequence of a (one color) $G$-operad,…
In this work, we present some elementary properties of Segal-Bargmann space and some properties of unitary Segal Bargmann transform with applications to differential operators arising out of diffusion problem or of reggeon field theory.
We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product H\"ormander spaces for which an RO-varying radial function serves as a regularity index. These spaces do not depend on a…
This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of $P(z)$-tensor products for nonzero complex numbers $z$ constructed…
We introduce a novel notion of pasting shapes for iterated Segal spaces which classify particular arrangements of composing cells in d-uple Segal spaces. Using this formalism, we then continue to prove a pasting theorem for these iterated…