# Definable and Non-definable Notions of Structure

@article{Swan2022DefinableAN, title={Definable and Non-definable Notions of Structure}, author={Andrew W. Swan}, journal={ArXiv}, year={2022}, volume={abs/2206.13643} }

Deﬁnability is a key notion in the theory of Grothendieck ﬁbrations that characterises when an external property of objects can be accessed from within the internal logic of the base of a ﬁbration. In this paper we consider a generalisation of deﬁnability from properties of objects to structures on objects, introduced by Shulman under the name local representability. We ﬁrst develop some general theory and show how to recover existing notions due to B´enabou and Johnstone as special cases. We…

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