2004•Electronic Notes in Theoretical Computer ScienceOpen access

Recursive Coalgebras from Comonads

Venanzio Capretta, Tarmo Uustalu, Varmo Vene

Abstract

We discuss Osius's [G. Osius, Categorical set theory: A characterisation of the category of sets, J. of Pure and Appl. Algebra 4 (1974) 79–119] concept of a recursive coalgebra of a functor from the perspective of programming semantics and give some new sufficient conditions for the recursiveness of a functor-coalgebra that are based on comonads, comonad-coalgebras and distributive laws.

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Key concepts: Coalgebra, Functor, Distributive property, Mathematics, Categorical variable, Category theory, Perspective (graphical), Algebra over a field