Galois theory in variable categories
The order reversing bijection between field extensions of \(K\) and subgroups of the Galois group \(G\) is a classical algebraic result. Grothendieck has shown that this bijection follows from the equivalence between the opposite of the category of étale algebras and the category of discrete \(G\)-spaces, throwing so a link between topos theory and classical Galois theory. This allowed extending Galois theory to more general rings and generalized spaces. In the present paper, the authors further generalize the Galois structures from ordinary categories to variable or indexed categories, so as to recapture in particular the well-known Joyal-Tierney theory, extending the Grothendieck Galois theory.
scientific article; zbMATH DE number 458992