An externally saturated class $\Sigma$ of morphisms in a category $\mathcal C $ is the class of morphisms that are inverted by some functor $F: \mathcal C \to \mathcal D$. On the other hand, $\Sigma$ is internally saturated if it coincides with its double orthogonal in the sense of Freyd-Kelly. In this short note we prove that $\Sigma\subset Mor\ \mathcal C $ is an internally saturated class if and only if it is externally saturated and admits a calculus of left fractions.
SATURATION FOR CLASSES OF MORPHISMS
STRAMACCIA, Luciano;
2010
Abstract
An externally saturated class $\Sigma$ of morphisms in a category $\mathcal C $ is the class of morphisms that are inverted by some functor $F: \mathcal C \to \mathcal D$. On the other hand, $\Sigma$ is internally saturated if it coincides with its double orthogonal in the sense of Freyd-Kelly. In this short note we prove that $\Sigma\subset Mor\ \mathcal C $ is an internally saturated class if and only if it is externally saturated and admits a calculus of left fractions.File in questo prodotto:
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