Geodesic
More on injectivity in locally presentable categories
Theory and applications of categories, Tome 10 (2002), pp. 148-161

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Injectivity with respect to morphisms having $\lambda$-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, $\lambda$-directed colimits, and $\lambda$-pure subobjects. This sharpens the result of the first two authors (Trans. Amer. Math. Soc. 336 (1993), 785-804). In contrast, for geometric logic an example is found of a class closed under directed colimits and pure subobjects, but not axiomatizable by a geometric theory. A more technical characterization of axiomatizable classes in geometric logic is presented.

Classification : 18C35, 03C99.
Keywords: locally presentable category, injectivity class, geometric logic. 
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     author = {J. Rosicky and J. Adamek and F. Borceux},
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J. Rosicky; J. Adamek; F. Borceux. More on injectivity in locally presentable categories. Theory and applications of categories, Tome 10 (2002), pp. 148-161. http://geodesic.mathdoc.fr/item/TAC_2002_10_a6/