Bilinearity and Cartesian Closed Monads.
Birkhoff's Covariety Theorem without limitations
J. Rutten proved, for accessible endofunctors of Set, the dual Birkhoff’s Variety Theorem: a collection of -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 of Set 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...
Birkhoff's variety theorem with and without free algebras.