Related papers: Compact Semisimple 2-Categories

In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…

We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…

We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

Let $A$ be a finite-dimensional algebra with two simple modules. It is shown that if the derived category of $A$ admits a stratification with simple factors being the base field $k$, then $A$ is derived equivalent to a quasi-hereditary…

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of…

The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this…

We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated…

We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these…

We generalize a recent result by J.F. Carlson to finite tensor categories having finitely generated cohomology. Specifically, we show that if the Krull dimension of the cohomology ring is sufficiently large, then there exist infinitely many…

We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and…

This paper is concerned with developing a 2-dimensional analogue of the notion of an ordinary discrete fibration. A definition is proposed, and it is shown that such discrete 2-fibrations correspond via a 2-equivalence to certain…

We use the terms "$\infty$-categories" and "$\infty$-functors" to mean the objects and morphisms in an "$\infty$-cosmos." Quasi-categories, Segal categories, complete Segal spaces, naturally marked simplicial sets, iterated complete Segal…

Let $k$ be a perfect field such that for every $n$ there are only finitely many field extensions, up to isomorphism, of $k$ of degree $n$. If $G$ is a reductive algebraic group defined over $k$, whose characteristic is very good for $G$,…

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…

We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetric monoidal as a bicategory.

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…