Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Groups of dualities


Authors: Georgi D. Dimov and Walter Tholen
Journal: Trans. Amer. Math. Soc. 336 (1993), 901-913
MSC: Primary 18A40; Secondary 18D05, 22D35, 54B30, 54H10
MathSciNet review: 1100693
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For arbitrary categories $ \mathcal{A}$ and $ \mathcal{B}$ , the "set" of isomorphism-classes of dualities between $ \mathcal{A}$ and $ \mathcal{B}$ carries a natural group structure. In case $ \mathcal{A}$ and $ \mathcal{B}$ admit faithful representable functors to Set, this structure can often be described quite concretely in terms of "schizophrenic objects" (in the sense of Johnstone's book on "Stone Spaces"). The general theory provided here allows for a concrete computation of that group in case $ \mathcal{A} = \mathcal{B} = \mathcal{C}$ is the category of all compact and all discrete abelian groups: it is the uncountable group of algebraic automorphisms of the circle $ \mathbb{R}/\mathbb{Z}$ , modulo its subgroup $ {\mathbb{Z}_2}$ of continuous automorphisms.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 18A40, 18D05, 22D35, 54B30, 54H10

Retrieve articles in all journals with MSC: 18A40, 18D05, 22D35, 54B30, 54H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1100693-0
Article copyright: © Copyright 1993 American Mathematical Society