Related papers: Perfect tangles
Perfect tensors are the tensors corresponding to the absolutely maximally entangled states, a special type of quantum states of interest in quantum information theory. We establish a method to compute parameterized families of perfect…
We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…
We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…
We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate…
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…
We introduce the notions of normal tensor functor and exact sequence of tensor categories. We show that exact sequences of tensor categories generalize strictly exact sequences of Hopf algebras as defined by Schneider, and in particular,…
We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum…
This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented…
We generalize the definition of an exact sequence of tensor categories due to Brugui\`eres and Natale, and introduce a new notion of an exact sequence of (finite) tensor categories with respect to a module category. We give three…
We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the…
We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a…
Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…
We give a parametrization of the ideal classes of rings associated to integral binary forms by classes of tensors in $\mathbb Z^2\tensor \mathbb Z^n\tensor \mathbb Z^n$. This generalizes Bhargava's work on Higher Composition Laws, which…
Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical…
We introduce several approaches to studying the Cantor-Bendixson decomposition of and the dynamics on the (topological) space of subgroups for various families of countable groups. In particular, we uncover the perfect kernel and the…
Motivated by applications to duality theorems for $p$-adic pro-\'etale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full…
The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this…
Let $(\mathcal{T}',\mathcal{T},\mathcal{T}'')$ be a recollement of triangulated categories.A complete ideal cotorsion pair in $\mathcal{T}$ induces complete ideal cotorsion pairs in $\mathcal{T}'$ and $\mathcal{T}''$. In addition, if…
We introduce a class of decorated abstract graphs, that we call XC-tangles, that provides a very convenient framework to study quantum invariants of tangles and virtual tangles. These can be viewed as a far-reaching generalisation of…
Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors have proven refined results, for example, extending all of…