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

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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” subHopfmonoids, 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 
MD5 Checksum of the PDFfile:  2729e1992f1aa1a8f1da017affa9b1c1 
Footnote:  Englische Übersetzung der deutschen Originalversion: GaloisTheorie in monoidalen Kategorien 
ID Code:  24952 
Deposited On:  21. Oct 2019 11:19 
Last Modified:  21. Oct 2019 11:19 