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Zbl 0842.18001
Sousa, Lurdes
Orthogonality and closure operators. (English)
[J] Cah. Topologie Géom. Différ. Catég. 36, No.4, 323-343 (1995). ISSN 0008-0004

The orthogonal hull $O({\cal A})$ of a full subcategory $\cal A$ in a category $\cal X$ is known to play an important role in the investigation of reflective subcategories [see {\it P. J. Freyd} and {\it G. M. Kelly}, J. Pure Appl. Algebra 2, 169-191 (1972; Zbl 0257.18005)] and the reviewer [Topology Appl. 27, 201-212 (1987; Zbl 0629.18004)]. The author gives a new approach to the computation of $O({\cal A})$ and provides conditions under which $O({\cal A})$ serves as the reflective hull $R({\cal A})$ of $\cal A$ in $\cal X$, via closure operators. Under suitable conditions on $\cal A$ and $\cal X$ she associates with $\cal A$ its so-called $\cal A$-orthogonal closure operator of $\cal X$, which exhibits the objects of $O({\cal A})$ as those objects of $\cal X$ that, when embedded into any other object, are closed. A sufficient condition for $O({\cal A}) = R({\cal A})$ follows and is carefully illustrated in terms of examples.
[W.Tholen (Downsview)]

MSC 2000:: *18A40 Adjoint functors
18A20 Special classes of morphisms
18B30 Categories of topological spaces
18A32 Factorization of morphisms

Keywords: orthogonal hull; reflective subcategories; reflective hull; orthogonal closure operator

Citations: Zbl 0257.18005; Zbl 0629.18004

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