Definition:Galois Connection/Also known as
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Definition
In some sources the upper adjoint is called the right adjoint and the lower adjoint is called the left adjoint.
The terminology right adjoint and left adjoint is also used to denote the functors of an adjuntion in the context of category theory.
So the use of the terms upper adjoint and lower adjoint for a Galois connection serves to differentiate the context of order theory from the context of category theory.
The mappings are named for the position that each mapping has with respect to the orderings involved in the defining condition of Galois connection.
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter II: Introduction to Locales, $\S1.1$
- 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter II: Frames and Locales. Spectra, $\S 2.2$