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On saturated classes of morphisms

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Carles Casacuberta and Armin Frei

The term ``saturated,'' referring to a class of morphisms
in a category, is used in the literature for two nonequivalent
concepts. We make precise the relationship between these two concepts
and show that the class of equivalences associated with any monad
is saturated in both senses.

Keywords: saturation, orthogonality, monad, shape, category of fractions.

2000 MSC: 18A40.

*Theory and Applications of Categories*, Vol. 7, 2000, No. 4, pp 43-46.

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