Related papers: Functors on triangulated tensor categories

We study the derived category of pseudo-coherent complexes over a noetherian commutative ring, building on prior work by Matsui-Takahashi. Our main theorem is a computation of the Balmer spectrum of this category in the case of a discrete…

We study oplax colimits of stable categories, of hermitian categories and of Poincar\'e categories in nice cases. This allows us to produce a categorical model of the assembly map of a bordism-invariant functor of Poincar\'e categories…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

We prove a thick subcategory theorem for the category of $d$-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=1$ case) and the $C_2$-equivariant thick subcategory theorem…

We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can…

We prove that the notion of Drinfeld center defines a functor from the category of indecomposable multi-tensor categories with morphisms given by bimodules to that of braided tensor categories with morphisms given by monoidal bimodules.…

We construct a functor from the category of elliptic curves to a category of noncommutative tori. Our proof is based on an isomorphism between the Sklyanin algebras and dense sub-algebras of the noncommutative tori.

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

The main objective of the present paper is to present a version of the Tannaka-Krein type reconstruction Theorems: If $F:B\to C$ is an exact faithful monoidal functor of tensor categories, one would like to realize $B$ as category of…

Following the theory of tensor triangular support introduced by Sanders, which generalizes the Balmer-Favi support, we prove the local version of the result of Zou that the Balmer spectrum being Hochster weakly scattered implies the…

We construct the categories of standard vector bundles over schemes and define direct sum and tensor product. These categories are equivalent to the usual categories of vector bundles with additional properties. The tensor product is…

We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of…

We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral $G$-Mackey functors for all finite groups $G$. Our…

It is constructed the functor from category of product linear space to category of skew-symmetric tensor space. It is defined and described the bound bundle as analog of a symplex and as basis element of new constructive homology theory.

We introduce a new type of categorical object called a \emph{hom-tensor category} and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided category} and…

We prove that any derived equivalence between triangular algebras is standard, that is, it is isomorphic to the derived tensor functor given by a two-sided tilting complex.

We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational…

We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances in algebra and geometry where abelian, exact…

We prove that etale morphisms of schemes yield separable extensions of derived categories. We then generalize the Neeman-Thomason Localization Theorem to separable extensions of triangulated categories.