Related papers: On normal tensor functors and coset decompositions…
In this paper, we define the functor category Fquad associated to vector spaces over the field with two elements, F\_2, equipped with a quadratic form. We show the existence of a fully-faithful, exact functor \iota: \F \to Fquad, which…
We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…
For a category $\mathbb{C}$, a small category $\mathbb{I}$, and a pre-cover relation $\sqsubset$ on $\mathbb C$ we prove, under certain completeness assumptions on $\mathbb C$, that a morphism $g: B\to C$ in the functor category $\mathbb…
Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…
Suppose $\mathcal{E}$ is a normal subsystem of a saturated fusion system $\mathcal{F}$ over $S$. If $X\leq S$ is fully $\mathcal{F}$-normalized, then Aschbacher defined a normal subsystem $N_{\mathcal{E}}(X)$ of $N_{\mathcal{F}}(X)$. In…
We consider families of quasisymmetric functions with the property that if a symmetric function $f$ is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions. Furthermore, in each of…
We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we obtain two corollaries concerning meromorphic functions $f \colon {\mathbb C} \to {\widehat{\mathbb C}}$: i)…
We propose a framework for fusion category symmetry on the (1+1)D lattice in the infinite-volume limit by giving a formal interpretation of SymTFT decompositions. Our approach is based on axiomatizing physical boundary subalgebra of…
In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$…
In previous work, we defined the category of functors Fquad, associated to vector spaces over the field with two elements equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category…
This is a PhD Thesis on the connection between subfactors (more precisely, their corresponding fusion categories) and Conformal Field Theory (CFT). Besides being a mathematically interesting topic on its own, subfactors have also attracted…
The purpose of this article is threefold: Firstly, we propose some enhancements to the existing definition of 6-functor formalisms. Secondly, we systematically study the category of kernels, which is a certain 2-category attached to every…
We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is…
The main purpose of this paper is to introduce the random tensor with normal distribution, which promotes the matrix normal distribution to a higher order case. Some basic knowledge on tensors are introduced before we focus on the random…
In this paper we develop the theory of quasispaces (for a Grothendieck topology) and of concrete quasitopoi, over a suitable base category. We introduce the notion of f-regular category and of f-regular functor. The f-regular categories are…
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are…
This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…
We introduce the notion of $\lambda$-equivalence and $\lambda$-embeddings of objects in suitable categories. This notion specializes to $L_{\infty\lambda}$-equivalence and $L_{\infty\lambda}$-elementary embedding for categories of…
Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…
In their article "Elementary construction of perverse sheaves", R.MacPherson and K. Vilonen show that on a Thom-Mather space X the category PervX of perverse sheaves is equivalent to the category C(F, G, T) whose objects are data of…