Related papers: On functors associated to a simple root

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…

A general construction of Knop creates a symmetric monoidal category $\mathcal{T}(\mathcal{A},\delta)$ from any regular category $\mathcal{A}$ and a fixed degree function $\delta$. A special case of this construction are the Deligne…

A bivariant functor is defined on a category of *-algebras and a category of operator ideals, both with actions of a second countable group $G$, into the category of abelian monoids. The element of the bivariant functor will be…

We prove that for a large class of well-behaved cocomplete categories $\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\mathcal{E}$ of cocontinuous endofunctors of $\mathcal{C}$ coincide. This generalizes similar…

We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…

We prove that the simple root functors E and F appearing in the categorification of irreducible highest weight modules of quantum groups via cyclotomic Khovanov-Lauda-Rouquier algebras is a biadjoint pair.

This article studies the categorical setting of Abramsky, Haghverdi, and Scott's untyped linear combinatory algebras, and relates this to more recent work of Abramsky and Heunen on Frobenius algebras in the infinitary setting. The key to…

We associate to an arbitrary positive root $\alpha$ of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor $T_\alpha$ of the category of $\mfrak{g}$-modules. We apply this functor to generalized Verma…

Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the…

Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of…

Morphisms in the linear category A of Jacobi diagrams in handlebodies give rise to interesting contravariant functors on the category gr of finitely-generated free groups, encoding part of the composition structure of the category A. These…

In category theory, monads, which are monoid objects on endofunctors, play a central role closely related to adjunctions. Monads have been studied mostly in algebraic situations. In this dissertation, we study this concept in some…

The main result concerns a bicategorical factorization system on the bicategory $\mathrm{Cat}$ of categories and functors. Each functor $A\xra{f} B$ factors up to isomorphism as $A\xra{j}E\xra{p}B$ where $j$ is what we call an ultimate…

Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to…

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…

Kato has constructed reflection functors for KLR algebras which categorify the braid group action on a quantum group by algebra automorphisms. We prove that these reflection functors are monoidal.

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…

We introduce the theory of biset functors defined on finite categories. Previously, biset functors have been defined on groups, and in that context they are closely related to Mackey functors. Standard examples on groups include…

Let $\mathfrak{g}_0$ be a simple Lie algebra of type ADE and let $U'_q(\mathfrak{g})$ be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group $B(\mathfrak{g}_0)$ on the quantum…

The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There…