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Closure operators with respect to a functor. (English) Zbl 1004.18002

For a functor \(U:{\mathcal A}\to X\) into a category \({\mathcal X}\) with a factorization structure, the paper introduces a categorical notion of closure operator for subobjects in \({\mathcal X}\) of objects of type \(UA\). When applied in the case that \(U\) is the identity functor, it coincides with the notion introduced by D. Dikranjan and E. Giuli [Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)]. The authors discuss basic properties and examples outsize the reach of the previous notion.

MSC:

18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
06A15 Galois correspondences, closure operators (in relation to ordered sets)
18A22 Special properties of functors (faithful, full, etc.)
54B30 Categorical methods in general topology

Citations:

Zbl 0634.54008
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