More on injectivity in locally presentable categories

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Authors

ROSICKÝ J. ADÁMEK J. BORCEUX F.

Year of publication 2002
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords locally presentable category; injectivity class
Description Injectivity with respect to morphisms having k-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, k-directed colimits and k-pure subobjects. This sharpens the result of the first two authors. 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.
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