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Final Dialgebras: From Categories to Allegories

Roland Backhouse, Paul Hoogendijk (2010)

RAIRO - Theoretical Informatics and Applications

The study of inductive and coinductive types (like finite lists and streams, respectively) is usually conducted within the framework of category theory, which to all intents and purposes is a theory of sets and functions between sets. Allegory theory, an extension of category theory due to Freyd, is better suited to modelling relations between sets as opposed to functions between sets. The question thus arises of how to extend the standard categorical results on the existence of final objects...

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