Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T08:11:35.929Z Has data issue: false hasContentIssue false
  • English
  • Français

Bialgebraic contexts from dualities

Part of: Other classes of algebra Abelian categories

Published online by Cambridge University Press:  09 April 2009

Keith A. Kearnes  and
Frank Vogt
Keith A. Kearnes
Affiliation:
Department of Mathematical SciencesUniversity of ArkansasFayetteville, AR 72701USA e-mail: [email protected]
Frank Vogt
Affiliation:
Fachbereich Mathematik Technische HochschuleDarmstadt Schoßgartenstraß 7 D-64289 DarmstadtGermany e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we show that a bialgebraic context which arises from a duality in a fairly general way must arise from a duality between categories of modules. To show this, we give an elementary proof of Mitchell's Embedding Theorem for prevarieties.

MSC classification

Secondary: 08C05: Categories of algebras 18E20: Embedding theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 389 - 404
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Anderson, F. W. and Fuller, K. R., Rings and categories of modules (Springer, New York, 1974).CrossRefGoogle Scholar
[2]Clark, D. M. and Davey, B. A., ‘When is a natural duality “good”? Algebra Universalis, to appear.Google Scholar
[3]Davey, B. A., ‘Duality theory on ten dollars a day’, in: Algebras and orders (eds. Rosenberg, I. G. and Sabidussi, G.) (Kluwer Academic Publishers, Dordrecht, 1993), pp. 71–111.CrossRefGoogle Scholar
[4]Davey, B. A. and Werner, H., ‘Dualities and equivalences for varieties of algebras’, Colloquia Mathematica Societatis J´nos Bolyai 33 (1983), 101–275.Google Scholar
[5]Freese, R. and McKenzie, R., Commutator theory for congruence modular varieties, London Math. Soc. Lecture Notes 125 (Cambridge University Press, 1987).Google Scholar
[6]Ganter, B. and Wille, R., ‘Conceptual scaling’, in: Applications of combinatorics and graph theory to the biological and social sciences (ed. Roberts, F.) (Springer, New York, 1989) pp. 139–167.CrossRefGoogle Scholar
[7]McKenzie, R., McNulty, G. and Taylor, W., Algebras, lattices, varieties, volume I (Wadsworth and Brooks/Cole, Monterey, 1987).Google Scholar
[8]Mitchell, B., Theory of categories (Academic Press, 1965).Google Scholar
[9]Vogt, F., Bialgebraic contexts (Ph. D. Thesis, TH Darmstadt, 1994; printed version: Shaker, Aachen, 1994).Google Scholar
[10]Vogt, F. and Wille, R., ‘Ideas of algebraic concept analysis’, in: Information systems and data analysis (eds. Bock, H.-H., Lenski, W. and Richter, M. M.) (Springer, Heidelberg, 1994) pp. 193–205.Google Scholar
[11]Wille, R., ‘Restructuring lattice theory: an approach based on hierarchies of concepts’, in: Ordered sets (ed. Rival, I.) (Reidel, Dordrecht, 1982) pp. 445–470.CrossRefGoogle Scholar