Related papers: Tannakian categories: origins and summary

The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such examples are called `algebraic' because they originate from abelian…

In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.

We study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor…

Based on a new theory of causality [1] and its development to the theory of the Universe [2], we show, in this paper, new ideas for building a theory of everything.

We review some of the basic mathematical results about density functional theory.

In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.

We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.

This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be divided into four parts: The first part is an introduction to the theory of monomorphism categories, including a short survey on some representation…

A brief presentation of basic definitions and notation used in permutation patterns research.

$n$-exangulated categories were introduced by Herschend-Liu-Nakaoka which are a simultaneous generalization of $n$-exact categories and $(n+2)$-angulated categories. This paper consists of two results on $n$-exangulated categories: (1) we…

In this talk I make some remarks about the search for the origin of the electroweak scale.

This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

How did star formation begin in the universe? Some of the questions addressed at this first meeting on "The First Stars" are summarized here from a theoretical perspective, and some brief comments are made on what we may have learned so…

We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…

We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more…

Given a rigid tensor-triangulated category and a vector space valued homological functor for which the K\"{u}nneth isomorphism holds, we construct a universal graded-Tannakian category through which the given homological functor factors. We…

K. S. S. Nambooripad introduced an interesting class of categories known as normal categories, which are categories with subobjects, morphisms admitting factorization and having sufficiently many cones. These normal categories plays…

A generalization of the notion of an $\infty$-category is presented, allowing for ($\infty$-)cat(egorie)s that may have non-invertible higher morphisms.

I propose a notion of theory motivated by Category theory.