Sorry, maybe I ought to have been more explicit about "By the Galois Connection between G and C.": https://ncatlab.org/nlab/show/Galois+connection#GaloisTheory

Sorry, maybe I ought to have been more explicit about "By the Galois Connection between G and C.": https://ncatlab.org/nlab/show/Galois+connection#GaloisTheory https://ncatlab.org/nlab/show/Galois+connection#GaloisTheory > The Galois theory normally taught in graduate-level algebra courses ... involves a Galois connection between the intermediate fields of a Galois extension and the subgroups of the corresponding Galois group. Instead of speaking informally, of abuse of Galois Theory, I should have spoken formally, of abstraction of Galois Theory. Does it make more sense now?