Related papers: Segalification and the Boardman-Vogt tensor produc…
We construct a generalization of the Day convolution tensor product of presheaves that works for certain double $\infty$-categories. Using this construction, we obtain an $\infty$-categorical version of the well-known description of…
Classical Segal-Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and the configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued…
We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…
The description of algebraic structure of n-fold loop spaces can be done either using the formalism of topological operads, or using variations of Segal's $\Gamma$-spaces. The formalism of topological operads generalises well to different…
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
We propose a construction of the monoidal envelope of $\infty$-operads in the model of Segal dendroidal spaces, and use it to define cocartesian fibrations of such. We achieve this by viewing the dendroidal category as a "plus construction"…
We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-wise eigenvalues, instead of scalar eigenvalues as in the…
Following work of Brundan and Kleshchev (2000), which considered tensor products with the natural module (and its dual) for $\text{GL}(n)$, we take the next fundamental module and explore the relationship between multiplicities of…
The d-Segal conditions of Dyckerhoff and Kapranov are exactness properties for simplicial objects based on the geometry of cyclic polytopes in d-dimensional Euclidean space. 2-Segal spaces are also known as decomposition spaces, and most…
Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories.…
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity…
In this paper we give a model for equivariant $(\infty, 1)$-categories. We modify an approach of Shimakawa for equivariant $\Gamma$-spaces to the setting of simplicial spaces. We then adapt Rezk's Segal and completeness conditions to fit…
This is an expository note on Fedosov's construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive…
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to…
We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present…
We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman equivalence. Using this, some new formulas for cohomological invariants of these…
We generalize a construction of Bell and Rogalski to realize new examples of $\mathbb{Z}^n$-graded simple rings. This construction also generalizes TGWAs of type $(A_1)^n$. In addition to considering basic properties of these algebras, we…
We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or…