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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;]
Published on May 28, 2021

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;]
Published on August 9, 2013

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;]
Published on November 8, 2006

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