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K-purity and orthogonality
Theory and applications of categories, Tome 12 (2004), pp. 355-371 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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Adamek and Sousa recently solved the problem of characterizing the subcategories K of a locally $\lambda$-presentable category C which are $\lambda$-orthogonal in C, using their concept of K$\lambda$-pure morphism. We strengthen the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to $\lambda$-presentable morphisms (where $f : A \rightarrow B is called $\lambda$-presentable if it is a $\lambda$-presentable object of the comma category A/$\lambda$-presentable morphisms are precisely the pushouts of morphisms between $\lambda$-presentable objects of C.

Classification : 18A20, 18C35, 03C60, 18G05
Keywords: pure morphism, othogonality, injectivity, locally presentable categories, accessible categories 
@article{TAC_2004_12_a11,
     author = {Michel Hebert},
     title = {K-purity and orthogonality},
     journal = {Theory and applications of categories},
     pages = {355--371},
     year = {2004},
     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_12_a11/}
}
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Michel Hebert. K-purity and orthogonality. Theory and applications of categories, Tome 12 (2004), pp. 355-371. http://geodesic.mathdoc.fr/item/TAC_2004_12_a11/