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arXiv · 2009.14023

General facts on the Scott Adjunction

Ivan Di Liberti
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Abstract

We introduce, comment and develop the Scott adjunction, mostly from the point of view of a category theorist. Besides its technical and conceptual aspects, in a nutshell we provide a categorification of the Scott topology over a posets with directed suprema. From a technical point of view we establish an adjunction between accessible categories with directed colimits and Grothendieck topoi. We show that the bicategory of topoi is enriched over the $2$-category of accessible categories with directed colimits and it has tensors with respect to this enrichment. The Scott adjunction (ri-)emerges naturally from this observation.

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Ivan Di Liberti. 2021-12-09. General facts on the Scott Adjunction. https://doi.org/10.1007/s10485-021-09666-6

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