Related papers: A representability theorem for some huge abelian c…
To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we…
We define the spectrum of a tensor triangulated category $K$ as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects…
We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let $\mathscr{X}$ denote an additive category with finite direct sums and split…
The Frobenius-Perron theory of an endofunctor of a category was introduced in recent years [12, 13]. We apply this theory to monoidal (or tensor) triangulated structures of quiver representations.
The main result of this paper may be stated as a construction of "almost representations" for the canonical presheaves of object extensions of length n on the C-systems defined by locally cartesian closed universe categories with binary…
For a split reductive group $G$ over a finite extension $L$ of ${\mathbb Q}_p$, and a parabolic subgroup $P \subset G$ we introduce a category ${\mathcal O}^P$ which is equipped with a forgetful functor to the parabolic category ${\mathcal…
We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left…
For an abelian category C and a filtrant preordered set Lambda, we prove that the derived category of the quasi-abelian category of filtered objects in C indexed by Lambda is equivalent to the derived category of the abelian category of…
A semi-localization of a category is a full reflective subcategory with the property that the reflector is semi-left-exact. In this article we first determine an abstract characterization of the categories which are semi-localizations of an…
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution…
Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S(X)=X[2]. As an application, this…
We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…
We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact categories and triangulated categories. Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an…
We prove a localisation theorem for the K-theory of filtering subcategories of exact $\infty$-categories which subsumes the localisation theorem for stable $\infty$-categories, Quillen's localisation theorem for abelian categories, and…
The Exel-Loring formula asserts that two topological invariants associated to a pair of almost commuting unitary matrices coincide. Such a pair can be viewed as a quasi-representation of $\mathbb{Z}^2$. We give a generalization of this…
A Tannakian category is an abelian tensor category equipped with a fiber functor and additional structures which ensure that it is equivalent to the category of representations of some affine groupoid scheme acting on the spectrum of a…
In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
This text collects useful results concerning the quasi-Hopf algebra $\D $. We give a review of issues related to its use in conformal theories and physical mathematics. Existence of such algebras based on 3-cocycles with values in $ {R} /…
We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…