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A Categorical Approach to Syntactic Monoids

Jiří Adamek ; Stefan Milius ; Henning Urbat.

The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category $\mathcal D$. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott ($\mathcal D=$ sets), the&nbsp;[&hellip;]

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Elgot Algebras

Jiri Adamek ; Stefan Milius ; Jiri Velebil.

Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive&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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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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