Functors on the category of quasi-fibrations

We consider the following questions: when can we extend a continuous endofunctor on Top the category of topological spaces to a fibrewise continuous endofunctor on Top(2) the category of continuous maps? If this is true, does such fibrewise continuous endofunctor preserve fibrations? In this paper, we define Fib the topological category of cell-wise trivial fibre spaces over polyhedra and show that any continuous endofunctor on Top induces a fibrewise continuous endofunctor on Fib preserving the class of quasi-fibrations.     

Irreducible morphisms in the bounded derived category

We study irreducible morphisms in the bounded derived category of finitely generated modules over an Artin algebra Λ, denoted , by means of the underlying category of complexes showing that, in fact, we can restrict to the study of certain subcategories of finite complexes. We prove that as in the case of modules there are no irreducible morphisms from X to X if X is an indecomposable complex. In case Λ is a selfinjective Artin algebra we show that for every irreducible morphism f in either f^j is split monomorphism for all j∈Z or split epimorphism, for all j∈Z. Moreover, we prove that all the non-trivial components of the Auslander-Reiten quiver of are of the form ZA_∞.     

Composite of irreducible morphisms in the bounded derived category

We study necessary and sufficient conditions for the existence of n irreducible morphisms in the bounded derived category of an Artin algebra, with non-zero composite in the n+1-power of the radical. In the case of , the bounded derived category of an Ext-finite hereditary k-category with tilting object, such irreducible morphisms exist if and only if H is derived equivalent to a wild hereditary algebra or to a wild canonical algebra. We also characterize the cluster tilted algebras having such irreducible morphisms.     

The dirichlet problem in a domain whose boundary is partly degenerated

Summary In this paper we bring a formulation of the Dirichlet problem for strongly elliptic equations in domains vhose boundaries may include manifolds of different dimensions. It is shown that, under certain regularity conditions, this problem is equivalent to the generalized Dirichlèt problem, with respect to existence and uniquennes of solutions. This paper represents part of a thesis submitted to the Senate of the Technion, Israel Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Science. The author wishes to tank ProfessorS. Agmon for his gudance and help in the preparation of this work.     

Functors of the category of abelian sheaves on regular affine scheme

In this short paper, we prove that ifR is a regular local ring of unequal characteristic, then there exists an additive covariant functorG from the category of abelian sheaves on SpecR to the category of abelian groups such that id _R (G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.     

On the category of weak Cayley table morphisms between groups

Weak Cayley table functions between groups are generalized conjugacy-preserving homomorphisms, under which products of images are conjugate to images of products. There is a weak Cayley table bijection between two groups iff they have the same 2-characters. In this paper, weak Cayley table functions are augmented to include the specific conjugating elements, leading to the concept of a weak (Cayley table) morphism. If the conjugating elements are chosen subject to a crossed-product condition, then the weak morphisms between groups form a category. The forgetful functor to this category from the category of group homomorphisms is shown to possess a left adjoint. Two weak morphisms are said to be homotopic if they project to the same weak Cayley table function. As a first step in the analysis of the category of weak morphisms, the group of units of the monoid of weak morphisms homotopic to the identity automorphism of a group is described.     

A characterization of varieties whose universal cover is the polydisk or a tube domain

In this article we give necessary and sufficient conditions, in terms of certain tensors called semispecial tensors, respectively slope zero tensors, in order that the universal covering of a complex projective manifold be a symmetric domain of tube type. As an application, we give precisions of a result of Kazhdan showing that a Galois conjugate of such a manifold has the same universal covering.     

Martin boundary of a plane domain,whose complement is situated on the line

Translated from Matematicheskie Zametki, Vol. 47, No. 2, pp. 20–27, February, 1990.     

Images and preimages of subobjects under the morphisms in a new category of fuzzy sets-I

This paper is the third in a sequence of papers on categories by the same authors. In one of the papers, a new category of fuzzy sets was defined and a few results were established pertaining to that special category of fuzzy sets S. Here, the concept of a fuzzy subset of a fuzzy set is defined under the category S. Besides, the notions of images and preimages of fuzzy sets are also defined under morphisms in the category of fuzzy sets and how smoothly these images and preimages behave under the action of these morphisms is analyzed. Finally, results have been proved on algebra of morphisms of this category S.     

Nonlocal problem for an equation of mixed type in a domain whose elliptic part is a half-strip

For the Gellerstedt equation, we study a problem with shift in a domain whose elliptic part is an infinite half-strip. By using generalized fractional differentiation operators, we specify a linear combination that relates the value of the solution on characteristics of the equation with the value of the solution and its derivative on the parabolic degeneration line. We prove the unique solvability of this problem.     

The coherent homotopy category over a fixed space is a category of fractions

In this note we prove that the coherent homotopy category over a fixed space B with morphisms represented by certain homotopy commutative squares (see [8]) is isomorphic to the category obtained by formally inverting those maps in the category Top_B of topological spaces over B which are ordinary homotopy equivalences.     

Stratifications and Mackey Functors I: Functors For a Single Group

In the context of Mackey functors we introduce a category whichis analogous to the category of modules for a quasi-hereditaryalgebra which have a filtration by standard objects. Many ofthe constructions which work for quasi-hereditary algebras canbe done in this new context. In particular, we construct ananalogue of the ‘Ringel dual’, which turns out hereto be a standardly stratified algebra. The Mackey functors whichplay the role of the standard objects are constructed in thesame way as functors which have been used previously in parametrizingthe simple Mackey functors, but instead of using simple modulesin their construction (as was done before) we use p-permutationmodules. These Mackey functors are obtained as adjoints of theoperations of forming the Brauer quotient and its dual. Thefiltrations which have these Mackey functors as their factorsare closely related to the filtrations whose terms are the sumof induction maps from specified subgroups, or are the commonkernel of restriction maps to these subgroups. These latterfiltrations appear in Conlon's decomposition theorems for theGreen ring, as well as in other places, where they arise quitenaturally. 2000 Mathematics Subject Classification: primary 20C20; secondary20J05, 19A22, 16G70, 16E60.     

On semirings whose additive reduct is a semilattice

A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x∈S such that a+axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e∈S is a k-idempotent if e+e ²=e ². Basic properties of k-regular semirings whose k-idempotents are commutative have been studied.