On 09/11/16 10:48, Thomas Streicher wrote:
What Eduardo means by "Giraud topos" is a category validating all conditions of the Giraud theorem with the exception of having a small generating family. These guys can be elementary toposes or not. There is Freyd's example where objects are set X with an ordinal indexed family of bijections from X to X
So they don't form a class. Is there an example where the objects form a class? (I like categories to have this property!) Paul
and morphisms are maps commuting with elementary topos lacking a s mall generating family. In 2011 on this list Johnstone gave the example of a category which superficially is like Freyd's example but the class many endomaps are not required to be bijections. This category is also bicomplete and locally small but it hasn't got a subobject classifier.
Thomas
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