Galois theory in monoidal categories

Ligon, Thomas S. (1978): Galois theory in monoidal categories. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics

Abstract

The Galois theory of Chase and Sweedler [11], for commutative rings, is generalized to encompass commutative monoids in an arbitrary symmetric, closed, monoidal category with finite limits and colimits. The primary tool is the Morita theory of Pareigis [35, 36, 37], which also supplies a suitable definition for the concept of a “finite” object in a monoidal category. The Galois theory is then extended by an examination of “normal” sub-Hopf-monoids, and examples in various algebraic and topological categories are considered. In particular, symmetric, closed, monoidal structures on various categories of topological vector spaces are studied with respect to the existence of “finite” objects.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Galois theory, monoidal categories
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 510 Mathematics
• Faculties: Faculty of Mathematics, Computer Science and Statistics
• Language: English
• Date of oral examination: 24. May 1978
• 1. Referee: Pareigis, Bodo

Footnote

Englische Übersetzung der deutschen Originalversion: Galois-Theorie in monoidalen Kategorien