Weakly hereditary initial closure operators
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.
APPLIED CATEGORICAL STRUCTURES
Fay, T. H.
(2000). Weakly hereditary initial closure operators. APPLIED CATEGORICAL STRUCTURES, 8(1-2), 415-431.
Available at: http://aquila.usm.edu/fac_pubs/4218