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The semireflexive product of two subcategories


Author: Cerbu Olga
Degree:doctor of physics and mathematics
Speciality: 01.01.06 - Mathematical logics, algebra and theory of numbers
Year:2012
Scientific consultant: Dumitru Botnaru
doctor habilitat, associate professor (docent), Tiraspol State University
Institution: Moldova State University
Scientific council: DH 01-01.01.06
Institute of Mathematics and Computer Science of the ASM

Status

The thesis was presented on the 25 August, 2012
Approved by NCAA on the 9 October, 2012

Abstract

Adobe PDF document – 0.25 Mb / in romanian

Keywords

the reflector and coreflector functor, the left exact reflector functor, semireflexive spaces, semireflexive subcategories, the semireflexive product of two subcategories, the right product of two subcategories

Summary

Thesis structure: the thesis is written in romanian and consist of an introduction, 3 chapters, conclusions, 116 bibliography titles, 128 pages of main text and 70 figures. Obtained results are published in 10 scientific papers.

Field of study of the thesis: Category theory with construction of examples in functional analysis.

The aim of research: Defining and studying the semireflexive subcategories properties and establishing the relation between semireflexive subcategories with right product and with the pairs of conjugated categories. Deriving aims that consist of studying relation of the reflector functors with the factorization structures, examining the properties of the left exact functors, researching of the completion functors.

Scientific innovation and originality: The main problem consists of development of the semireflexive product concept of two subcategories and studying the properties of this product, in dependence of the factors properties. The scientific innovation of the thesis is determined by solving of the next problems: were examined the reflector functors which preserve or reflect classes of morphism of the factorization structures; were examined the left exact reflector functors; were constructed the left exact completion functors; were defined the semireflexive product of two subcategories; were studied the properties of the semireflexive subcategories; were set the relation of this subcategories with the right product and with pairs of conjugated subcategories.

The main scientific resolved problem: developing the concept of the semireflexive product of two subcategories and studying the properties of this product in dependence of the properties of the factors.

The theoretical significance and applicative value of the thesis: were developed concepts, methods and new constructions which have contributed to objectives. They permitted the solution of concrete problems: were described the left exact functors; was established that any semireflexive subcategory is the result of a right product.

The implementation of the scientific results: Was established the concept of the semireflexive product of two subcategories and was developed the theory of this concept. 6