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A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

Category Theory · Mathematics 2007-05-23 Ingo Runkel , Jurgen Fuchs , Christoph Schweigert

Frobenius monoidal functors preserve duals. We show that conversely, (co)monoidal functors between autonomous categories which preserve duals are Frobenius monoidal. We apply this result to linearly distributive functors between autonomous…

Category Theory · Mathematics 2014-07-15 Adriana Balan

This expository article presents a unified ring theoretic approach, based on the theory of Frobenius algebras, to a variety of results on Hopf algebras. These include a theorem of S. Zhu on the degrees of irreducible representations, the…

Rings and Algebras · Mathematics 2010-08-25 Martin Lorenz

We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric…

Algebraic Topology · Mathematics 2017-10-03 Thomas Nikolaus , Steffen Sagave

The classification of (proper) compactifications of topological groups with respect to the possibility of extensions of algebraic operations is presented. Ellis' method of construction compactifications of topological groups allows one to…

General Topology · Mathematics 2025-07-29 K. L. Kozlov , A. G. Leiderman

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…

Group Theory · Mathematics 2015-05-27 Adam S. Sikora

We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if…

Number Theory · Mathematics 2007-05-23 C. S. Rajan

Given a right exact functor from an abelian category into another abelian category, there is an associated abelian category called the comma category of the functor. In this paper, we characterize when left Frobenius pairs (resp. strong…

Rings and Algebras · Mathematics 2023-10-23 Yajun Ma , Dandan Sun , Rongmin Zhu , Jiangsheng Hu

Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.

Classical Analysis and ODEs · Mathematics 2015-07-07 Elza Farkhi , Tzanko Donchev , Robert Baier

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…

Functional Analysis · Mathematics 2015-02-12 Marco Falconi

An open problem with categorical compositional distributional semantics is the representation of words that are considered semantically vacuous from a distributional perspective, such as determiners, prepositions, relative pronouns or…

Computation and Language · Computer Science 2016-08-05 Dimitri Kartsaklis

Given a hypercube of Frobenius extensions between commutative algebras, we provide a diagrammatic description of some natural transformations between compositions of induction and restriction functors, in terms of colored…

Representation Theory · Mathematics 2017-01-11 Ben Elias , Noah Snyder , Geordie Williamson

In this paper we define a rigid rational homotopy type, associated to any variety $X$ over a perfect field $k$ of positive characteristic. We prove comparison theorems with previous definitions in the smooth and proper, and log-smooth and…

Number Theory · Mathematics 2017-01-25 Christopher Lazda

We provide a new description of the hom functor on weak $\omega$-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a…

Category Theory · Mathematics 2024-11-14 Thibaut Benjamin , Ioannis Markakis

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…

Quantum Algebra · Mathematics 2020-06-04 Petter Andreas Bergh , Julia Yael Plavnik , Sarah Witherspoon

We study topological full groups attached to groupoid models for left regular representations of Garside categories. Groups arising in this way include Thompson's group $V$ and many of its variations such as R\"over-Nekrashevych groups. Our…

Operator Algebras · Mathematics 2024-10-15 Xin Li

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

Category Theory · Mathematics 2008-11-26 Ingo Runkel , Jens Fjelstad , Jurgen Fuchs , Christoph Schweigert

We define the notions of unital/counital/biunital infinitesimal anti-symmetric bialgebras and coFrobenius bialgebras and discuss their algebraic properties. We also define the notion of a graded 2D open-closed TQFT. These structures arise…

Symplectic Geometry · Mathematics 2024-09-11 Kai Cieliebak , Alexandru Oancea

We give another proof of the fact that there is a dual equivalence between the $\infty$-category of monoidal $\infty$-categories with left adjoint oplax monoidal functors and that with right adjoint lax monoidal functors by constructing a…

Category Theory · Mathematics 2023-02-07 Takeshi Torii

This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it…

Group Theory · Mathematics 2021-01-19 Bernard Rybołowicz