On coalgebra based on classes

Authors:
Jiří Adámek;Stefan Milius;Jiří Velebil
Affiliations:
Institute of Theoretical Computer Science, Technical University, Braunschweig, Germany;Institute of Theoretical Computer Science, Technical University, Braunschweig, Germany;Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, 166 27 Prague, Czech Republic
Venue:
Theoretical Computer Science - Logic, semantics and theory of programming
Year:
2004

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Abstract

The category Class of classes and functions is proved to have a number of properties suitable for algebra and coalgebra: every endofunctor is set-based, it has an initial algebra and a terminal coalgebra, the categories of algebras and coalgebras are complete and cocomplete, and every endofunctor generates a free completely iterative monad. A description of a terminal coalgebra for the power-set functor is provided.