# The Scott adjunction

@article{DiLiberti2020TheSA, title={The Scott adjunction}, author={Ivan Di Liberti}, journal={arXiv: Category Theory}, year={2020} }

We introduce and study the Scott adjunction, relating accessible categories with directed colimits to topoi. Our focus is twofold, we study both its applications to formal model theory and its geometric interpretation. From the geometric point of view, we introduce the categorified Isbell duality, relating bounded (possibly large) ionads to topoi. The categorified Isbell duality interacts with the Scott adjunction offering a categorification of the Scott topology over a poset (hence the name…

## 2 Citations

### A short proof of Shelah's eventual categoricity conjecture for AEC's with amalgamation, under $GCH$

- Mathematics
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We provide a short proof of Shelah's eventual categoricity conjecture for abstract elementary classes (AEC's) with amalgamation, assuming the Generalized Continuum Hypothesis ($GCH$). The proof…

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