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Birkhoff's Covariety Theorem without limitations

Jiří Adámek — 2005

Commentationes Mathematicae Universitatis Carolinae

J. Rutten proved, for accessible endofunctors F of , the dual Birkhoff’s Variety Theorem: a collection of F -coalgebras is presentable by coequations ( = subobjects of cofree coalgebras) iff it is closed under quotients, subcoalgebras, and coproducts. This result is now proved to hold for all endofunctors F of provided that coequations are generalized to mean subchains of the cofree-coalgebra chain. For the concept of coequation introduced by H. Porst and the author, which is a subobject of a member...

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