Title

Weakly Hereditary Initial Closure Operators

Document Type

Article

Publication Date

5-1-2000

Department

Mathematics

Abstract

We extend some recent of M. M. Clementino (Topology and its Applications 49 (1993)) and of the author (Cahiers de Topologie et Geometrie Differentielle Categoriques XXXVII(4) (1996)) concerning when a regular closure operator is weakly hereditary. In this work, we study initial closure operators which include both regular and normal closure operators. Working in a quasi-additive regular category in which pullbacks of cokernels are cokernels, we characterize when they initial closure operators are weakly hereditary. For the category of all groups, we show that a non-trivial normal closure operator is never weakly hereditary.

Publication Title

Applied Categorical Structures

Volume

8

Issue

1-2

First Page

415

Last Page

431