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Distributivity of Categories of Coalgebras
by
Tobias Schröder
University of Marburg, Germany
Coauthors: H. Peter Gumm (University of Marburg), Jesse Hughes (Carnegie Mellon University)
We prove that for any Set-endofunctor F the category SetF of F-coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever SetF has finite products. The key for the development is the observation that F preserves preimages if and only if each F-homomorphism into a sum induces a split of its domain.
http://www.mathematik.uni-marburg.de/~tschroed
Date received: January 2, 2001
Copyright © 2001 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 # cafo-46.