# Extensions of flat functors and theories of presheaf type

@article{Caramello2014ExtensionsOF, title={Extensions of flat functors and theories of presheaf type}, author={Olivia Caramello}, journal={arXiv: Category Theory}, year={2014} }

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a characterization theorem providing necessary and sufficient semantic conditions for a theory to be of presheaf type. This theorem subsumes all the previous partial results obtained on the subject and has several corollaries which can be used in practice for testing…

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