On coalgebra based on classes

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.

Authors

• Jiřı́ Adámek
• Stefan Milius
• Jiřı́ Velebil

Keywords

• Category of classes
• Set-based endofunctor
• Terminal coalgebra
• Iterative monad