Martin Sleziak HAD-classes in epireflective subcategories of Top Introduction Heredity of AD-classes References Basic definitions Hereditary coreflective subcategories of Top A generalization – epireflective subcategories AD-classes and HAD-classes Subcategories of Top All subcategories are assumed to be full and isomorphism-closed. subcategory of Top = class of topological spaces closer under ...

Let R be a commutative ring. A full additive subcategory C of R-modules is triangulated if whenever two terms of a short exact sequence belong to C, then so does the third term. In this note we give a classification of triangulated subcategories of finitely generated modules over a principal ideal domain. As a corollary we show that in the category of finitely generated modules over a PID, thic...

BACKGROUND The category "atypical glandular cells" (AGC) in The Bethesda System (TBS) 2001 represents equivocal glandular atypia. The objective was to determine the clinical significance of diagnosing AGC using new TBS 2001 on Thin-Prep. There is scant information on the diagnosis of AGC and its outcome on ThinPrep using TBS 2001. METHODS 174 "ThinPrep" Pap tests reported as atypical glandula...

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

Given any additive category C with split idempotents, pseudokernels and pseudocokernels, we show that a subcategory B is coreflective if, only it precovering, closed under direct summands each morphism in has pseudocokernel belongs to B. We apply this result its dual to, among others, preabelian pretriangulated categories. As consequence, of it, precovering taking cokernels. On the other hand, ...