K-purity and Orthogonality
نویسنده
چکیده
Adámek and Sousa recently solved the problem of characterizing the subcategories K of a locally λ-presentable category C which are λ-orthogonal in C, using their concept of Kλ-pure morphism. We strenghten the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to λ-presentable morphisms (where f :A B is called λ-presentable if it is a λ-presentable object of the comma category (A ↓ C)). Those classes are natural examples of reflective subcategories defined by proper classes of morphisms. Adámek and Sousa’s result follows from ours. We also prove that λ-presentable morphisms are precisely the pushouts of morphisms between λ-presentable objects of C.
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