A logic of orthogonality
Archivum mathematicum, Tome 42 (2006) no. 4, pp. 309-334
Voir la notice de l'article provenant de la source Czech Digital Mathematics Library
A logic of orthogonality characterizes all “orthogonality consequences" of a given class $\Sigma $ of morphisms, i.e. those morphisms $s$ such that every object orthogonal to $\Sigma $ is also orthogonal to $s$. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes $\Sigma $ of morphisms such that all members except a set are regular epimorphisms and (b) for all classes $\Sigma $, without restriction, under the set-theoretical assumption that Vopěnka’s Principle holds. For finitary morphisms, i.e. morphisms with finitely presentable domains and codomains, an appropriate finitary logic is presented, and proved to be sound and complete; here the proof follows immediately from previous joint results of Jiří Rosický and the first two authors.
@article{ARM_2006__42_4_a0,
author = {Ad\'amek, Ji\v{r}{\'\i} and H\'ebert, M. and Sousa, L.},
title = {A logic of orthogonality},
journal = {Archivum mathematicum},
pages = {309--334},
publisher = {mathdoc},
volume = {42},
number = {4},
year = {2006},
mrnumber = {2283016},
zbl = {1156.18301},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2006__42_4_a0/}
}
Adámek, Jiří; Hébert, M.; Sousa, L. A logic of orthogonality. Archivum mathematicum, Tome 42 (2006) no. 4, pp. 309-334. http://geodesic.mathdoc.fr/item/ARM_2006__42_4_a0/