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Well-Pointed Coalgebras

Jiří Adámek ; Stefan Milius ; Lawrence S Moss ; Lurdes Sousa.

For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists&nbsp;[&hellip;]

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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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