Some aspects of topological Galois theory

We establish a number of results on the subject of the first author's topos-theoretic generalization of Grothendieck's Galois formalism. In particular, we generalize in this context the existence theorem of algebraic closures, we give a concrete description of the atomic completion of a small category whose opposite satisfies the amalgamation property, and we explore to which extent a model of a Galois-type theory is determined by its symmetries. (C) 2019 Published by Elsevier B.V