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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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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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