Characterization Of Epimorphisms Research Articles

Comparing monomorphisms and epimorphisms in pro and [formula omitted]-categories

Given a category pair ( C , D ) , where D is dense in C , the abstract coarse shape category Sh ( C , D ) * was recently founded. It is realized via the category pro * - D defined on the class of all inverse systems in D . In this paper monomorphisms and epimorphisms in the category pro * - C are considered, for various categories C . The characterizations of epimorphisms (monomorphisms) in the category pro * - C are given, provided C admits products (sums). Since, one may consider the category pro - C as a subcategory of pro * - C , we discuss in which cases an epimorphism (monomorphism) in pro - C is an epimorphism (monomorphism) in pro * - C as well. We answered this question affirmatively for a category C admitting products (sums). It is shown by examples that the answer is generally negative, i.e. there exists a certain category C and an epimorphism (monomorphism) in pro - C which is not an epimorphism (monomorphism) in pro * - C .

TEST OF EPIMORPHISM FOR FINITELY GENERATED MORPHISMS BETWEEN AFFINE ALGEBRAS OVER COMPUTATIONAL RINGS

In this paper, based on a characterization of epimorphisms of R-algebras given by Roby [15], we bring an algorithm testing whether a given finitely generated morphism f : A → B, where A and B are finitely presented affine algebras over the same Nœtherian commutative ring R, is an epimorphism of R-algebras or not. We require two computational conditions on R, which we call a computational ring.

A NOTE ON REGULAR AND EXTREYAL SUBOBJECTS

ABSTRACT In the general setting of a complete, well-powered category A, we define and study two universal closure operations: regularization and extremalization, by means of regular and extremal subobjects of A. respectively. A general theorem of characterization of epimorphisms in A is given. When A is an epireflective subcategory of TOP, such operations are shown to coincide with A-closure [11] and epiclosure [2]. respectively. In the topological contest, regularization and extremalization are studied in detail and compared with r-closure, defined in [13].

Homomorphisms of Affine and Projective Planes

An elementary treatment of homomorphisms between affine and projective planes leads to characterizations of epimorphisms, monomorphisms, and isomorphisms of these geometries.