General facts on the Scott Adjunction
Category Theory
2022-01-27 v3
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 -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.
Cite
@article{arxiv.2009.14023,
title = {General facts on the Scott Adjunction},
author = {Ivan Di Liberti},
journal= {arXiv preprint arXiv:2009.14023},
year = {2022}
}
Comments
Final version. Accepted by Applied Categorical Structures