Related papers: Exact sequences of Frobenius tensor categories

Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C.…

We construct a fully faithful functor from the category C_F of finite-dimensional representations of Felder's (dynamical) elliptic quantum group E_{tau,gamma}(gl(n)) to a cretain category D_B of (infinite-dimensional) representations of…

The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when everything respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and…

We generalize the construction of tensor categories of endomorphisms of a type III factor $M$ associated with a $G$-kernel, from the case of a discrete group $G$ to that of a compact second countable group. Our approach is based on the…

By showing the compatibility of folding almost positive roots and folding cluster categories, we prove that there is a one-to-one correspondence between seeds and tilting seeds in non-simply-laced finite cases.

Suppose $C$ is a smooth projective curve of genus 1 over a perfect field $F$, and $E$ is its Jacobian. In the case that $C$ has no $F$-rational points, so that $C$ and $E$ are not isomorphic, $C$ is an $E$-torsor with a class $\delta(C)\in…

Given a torsion pair $(\mathcal{T},\mathcal{F})$ in an abelian category $\mathcal{A}$ and its Happel-Reiten-Smal{\o} tilt $\mathcal{B}$, the equivalence of the realization functor $D^b({\mathcal B})\to D^b({\mathcal A})$ is determined by…

These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements…

Let $k$ be a commutative ring, let $\mathcal{C}$ be a small, $k$-linear, Hom-finite, locally bounded category, and let $\mathcal{B}$ be a $k$-linear abelian category. We construct a Frobenius exact subcategory…

Consider a locally cartesian closed category with an object I and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential…

We show certain standard constructions of the theory of Verdier triangulated categories to be valid in the Heller triangulated framework as well; viz. Karoubi hull, exactness of adjoints, localisation.

We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…

Let $\mathcal{C}$ be a finite tensor category with simple unit object, let $\mathcal{Z}(\mathcal{C})$ denote its monoidal center, and let $L$ and $R$ be a left adjoint and a right adjoint of the forgetful functor $U:…

Let $\mathcal{T}$ be an algebraic triangulated category and $\mathcal{C}$ an extension-closed subcategory with $\operatorname{Hom}(\mathcal{C}, \Sigma^{<0} \mathcal{C})=0$. Then $\mathcal{C}$ has an exact structure induced from exact…

Let $C$ be an additive category with cokernels and let Mod($C$) be the category of additive functors from $C^{op}$ to the category Ab of abelian groups. Let mod($C$) be the full subcategory of Mod($C$) consisting of coherent functors. In…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…

We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of $N$-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object…

A graded tensor category over a group $G$ will be called a strongly $G$-graded tensor category if every homogeneous component has at least one multiplicativily invertible object. Our main result is a description of the module categories…

We investigate the existence of left and right adjoints to the restriction functor in three categories of continuous representations of a topological group: discrete, linear complete and compact.