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Weakly Hereditary Initial Closure Operators

In: Papers in Honour of Bernhard Banaschewski

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  • Temple H. Fay

    (University of Southern Mississippi, Department of Mathematics)

Abstract

We extend some recent of M. M. Clementino (Topology and its Applications 49 (1993)) and of the author (Cahiers de Topologie et Géométrie Différentielle Catégoriques 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.

Suggested Citation

  • Temple H. Fay, 2000. "Weakly Hereditary Initial Closure Operators," Springer Books, in: Guillaume Brümmer & Christopher Gilmour (ed.), Papers in Honour of Bernhard Banaschewski, pages 415-431, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2529-3_25
    DOI: 10.1007/978-94-017-2529-3_25
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