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### Can we define geometric morphisms (between ETCS categories) elementarily?

The ETCS axioms give conditions on a category for it to be a category of sets. These axioms can be written out in first order language, resulting in a finite axiomatisation of the category of sets. ...

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### How do we compare models of ETCS?

The elementary theory of the category of sets (nLab) gives axioms on a category such that it is a category of sets. In answering this MO question I realised that we might have trouble comparing ...