Yoneda representations of flat functors and classifying toposes

TL;DR

This paper introduces a Yoneda-based technique for flat functors and applies it to characterize models in classifying toposes, bridging indexed category theory with topos theory.

Contribution

It presents a novel Yoneda representation method for flat functors and applies it to analyze models in classifying toposes, enhancing understanding of their structure.

Findings

Characterization of models in classifying toposes using the new technique

Connection established between models in Sh(C,J) and [C^op, Set]

Advancement in the application of indexed category theory to topos theory

Abstract

In this paper, we first introduce a technique that we call "Yoneda representation of flat functors", based on ideas from indexed category theory; then we provide applications of this technique to the theory of classifying toposes. Specifically, we obtain results characterizing the models of a theory classified by a topos of the form Sh(C,J) in terms of the models of a theory classified by the topos [C^op, Set].