相关论文: Tannakian categories: origins and summary

This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.

The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…

In this paper we introduce the models for $(\infty, n)$-categories which have been developed to date, as well as the comparisons between them that are known and conjectured. We review the role of $(\infty, n)$-categories in the proof of the…

This is half an overview article since what we describe here is essentially known. We describe $KK$-theory by generators and relations in a formal sum of formal products of $*$-homomorphisms and some synthetical morphisms. What comes out is…

We present an analysis of some constructions and arguments from the universe of T. G. Goodwillie's Calculus, in a general model theoretic setting.

In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category…

We give an explicit construction of the category Opetope of opetopes. We prove that the category of opetopic sets is equivalent to the category of presheaves over Opetope.

T*-categories are introduced as a ternary generalization of C*-categories. Their linking C*-categories are constructed and the Gelfand-Naimark representation theorems of Zettl for C*-ternary rings and for W*-ternary rings, are generalized…

We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.

We give a presentation of abelian class field theory.

Selected examples of possible origins of power-law distributions are presented.

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.

In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set…

We describe the ind- and pro- categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.

Let $G$ be a finite group. In this paper, we first introduce a new notion, so-called the Mackey double category of $G$. Then we prove that the category of Mackey double categories and the category of Mackey functors of $G$ are equivalent.

We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and…