a particular correspondence (typically) between two partially ordered sets ( posets)

In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).

a pair of adjoint functors between two categories

A Galois connection is then nothing but a pair of adjoint functors between two categories that arise from partially ordered sets.

In mathematics especially in order theory

In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).

between field theory and group theory

Galois theory provides a connection between field theory and group theory.