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Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, ON, Canada

Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University

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Algebraic real analysis
by
Peter Freyd
University of Pennsylvania

Categorical investigations have disclosed a theory for ``interval algebras''. Its intended model is the closed real interval, identifiable in many categories as-ironically-a final co-algebra. A major theorem is that every algebra of this finitely presented equational theory has a simple quotient and that any simple algebra appears uniquely as a subalgebra of the intended model. This acts as a powerful completeness theorem and allows one to recover-using algebraic techniques-what appears to be a good part of real analysis.

Date received: September 6, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-47.