A note on admissibility of closed Galois structures

Abstract

We present a new admissibility theorem for Galois structures in the sense of G. Janelidze. It applies to relative exact categories satisfying a suitable relative modularity condition, and extends the known admissibility theorem in the theory of generalized central extensions. We also show that our relative modularity condition holds in every relative exact Goursat category.

Mathematics Subject Classification (2010): 18A20, 18A22, 18A40, 18B10, 06C05.

Keywords: Galois structure, relative exact category, relative exact Goursat category, admissible Galois structure, regular epimorphism, modular lattice, relative modularity