Related papers: Representability theorems via metric techniques

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak…

We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t=0) and the derived category of coherent…

We propose a new framework for the study of homological properties for (compactly generated) triangulated categories such as regularity, finiteness of global or finitistic dimension, gorensteinness or injective generation and the relation…

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

We obtain a theorem which allows to prove compact generation of derived categories of Grothendieck categories, based upon certain coverings by localizations. This theorem follows from an application of Rouquier's cocovering theorem in the…

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.

It is well known that cohomology with compact supports is not a homotopy invariant but only a proper homotopy one. However, as the proper category lacks of general categorical properties, a Brown representability theorem type does not seem…

In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise…

This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…

Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…

We prove that any digraph Brown functor -- i.e. a contravariant functor from the homotopy category of finite directed graphs to the category of abelian groups, satisfying the triviality axiom, the additivity axiom, and the Mayer-Vietoris…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

We consider notions of metrized categories, and then approximate categorical structures defined by a function of three variables generalizing the notion of $2$-metric space. We prove an embedding theorem giving sufficient conditions for an…

We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence…

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…

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

The main goal of this paper is to establish close relations among sheaves of modules on atomic sites, representations of categories, and discrete representations of topological groups. We characterize sheaves of modules on atomic sites as…