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.
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Fay, T.H. (2000). Weakly Hereditary Initial Closure Operators. In: Brümmer, G., Gilmour, C. (eds) Papers in Honour of Bernhard Banaschewski. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2529-3_25
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DOI: https://doi.org/10.1007/978-94-017-2529-3_25
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