A recollement describes one triangulated category T as “glued together” from two others, S and U. The definition is not symmetrical in S and U, but this note shows how S and U can be interchanged when T has a Serre functor. A recollement of triangulated categories S, T, U is a diagram of triangulated functors S i∗ // T j∗ // i ||

The main purpose of this paper is to introduce the concept of (Γ, n)semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category (Γ, n)-semihypergrous and the category semigroups. Moreover, we introduce and study complete part. Finally, we obtain some new results and some fundamental theorems in this respect.

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T (n) be the telescope of a vn self map of a finite S–module of type n. The Periodicity Theorem of Hopkins and Smith implies that the Bousfield localization functor associated to T (n)∗...

The goal of this article is to construct a language of the ZF set theory and to develop a notational and conceptual base which facilitates a convenient usage of the language. and 2] provide the notation and terminology for this paper. For simplicity we adopt the following rules: k, n denote natural numbers, D denotes a non empty set, a is arbitrary, and p, q denote nite sequences of elements of...

The high-frequency part of spectrum electromagnetic waves propagating parallel to the external magnetic field is considered for macroscopically motionless plasmas with relativistic temperatures $T\sim m_{e}c^{2}$, where $m_{e}$ mass electron, $c$ speed light. analysis based on novel hydrodynamic model four equations material fields which can be combined in two vectors. These are concentration a...

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

Quantification theory, or first-order predicate logic, can be formulated in terms purely of predicate letters and a few predicate functors which attach t o predicates to form further predicates. Apart from the predicate letters, which are schematic, there are no variables. On this score the plan is reminiscent of the combinatory logic of Schonfinkel and Curry. Theirs, however, had the whole of ...

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(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 and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equiv...

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen equivalent to simplicial model categories. A simplicial model category provides higher order structure such as composable mapping spaces and homotopy colimits. We ...