General facts on the Scott adjunction

0557874 - MÚ 2023 RIV NL eng J - Journal Article
Di Liberti, Ivan
General facts on the Scott adjunction.
Applied Categorical Structures. Roč. 30, č. 3 (2022), s. 569-591. ISSN 0927-2852. E-ISSN 1572-9095
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : accessible categories * enriched categories * Scott adjunction * Scott topology
OECD category: Pure mathematics
Impact factor: 0.6, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s10485-021-09666-6

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 (re-)emerges naturally from this observation.
Permanent Link: http://hdl.handle.net/11104/0331722