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Corecursive Algebras, Corecursive Monads and Bloom Monads

Jiří Adámek ; Mahdie Haddadi ; Stefan Milius.

An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is&nbsp;[&hellip;]

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Semantics of Higher-Order Recursion Schemes

Jiri Adamek ; Stefan Milius ; Jiri Velebil.

Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in which the terminals are interpreted as continuous operations.&nbsp;[&hellip;]

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Algebraic cocompleteness and finitary functors

Jiří Adámek.

A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and, more generally, all precontinuous) set functors the initial algebra and terminal coalgebra are proved to carry a&nbsp;[&hellip;]

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