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Abstract(s)
Given a full and replete subcategory A of a category X, we present a new closure operator, which allows a characterization of the class of all morphisms to which A is orthogonal and of the orthogonal hull of A by means of density and closedness, respectively. Using this characterization, we obtain, inter
alia, conditions under which the orthogonal hull coincides with the reflective hull of A. We also explore the relationship between the closure operator introduced here and the regular closure operator.
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Keywords
reflective hull orthogonal hull orthogonal closure operator