Related papers: Compactness in abelian categories
We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of the theoretical-set…
We introduce (dual) relative CS-Rickart objects in abelian categories, as common generalizations of (dual) relative Rickart objects and extending (lifting) objects. We study direct summands and (co)products of (dual) relative CS-Rickart…
In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.
We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary…
A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and…
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of…
This is the third in a series math.AG/0312190, math.AG/0503029, math.AG/0410268 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (\sigma,\iota,\pi) is a finite collection of…
Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this…
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…
We study the notion of a bifibration in simplicial sets which generalizes the classical notion of two-sided discrete fibration studied in category theory. If $A$ and $B$ are simplicial sets we equip the category of simplicial sets over…
Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…
Let $A$ be a finite dimensional algebra and $D^b(A)$ be the bounded derived category of finitely generated left $A$-modules. In this paper we consider lengths of compact exceptional objects in $D^b(A)$, proving a sufficient condition such…
This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…
The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a…
Locally compact abelian groups are classified in which the sum of any two closed subgroups is itself closed. This amounts to reproving and extending results by Yu.~N.~Mukhin from 1970. Namely we contribute a complete classification of all…
We construct moduli spaces of objects in an abelian category satisfying some finiteness hypotheses. Our approach is based on the work of Artin-Zhang and the intrinsic construction of moduli spaces for stacks developed by…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…