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# More on injectivity in locally presentable categories

## J. Rosicky, J. Adamek and F. Borceux

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.

Keywords: locally presentable category, injectivity class, geometric logic.

2000 MSC: 18C35, 03C99.

Theory and Applications of Categories, Vol. 10, 2002, No. 7, pp 148-161.

http://www.tac.mta.ca/tac/volumes/10/7/10-07.dvi
http://www.tac.mta.ca/tac/volumes/10/7/10-07.ps
http://www.tac.mta.ca/tac/volumes/10/7/10-07.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/7/10-07.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/7/10-07.ps

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