Abstract and concrete categories
Abstract and concrete categories
Specification of abstract data types
Specification of abstract data types
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Equational and implicational classes of coalgebras
Theoretical Computer Science
On varieties and covarieties in a category
Mathematical Structures in Computer Science
Algebra ∩ coalgebra = presheaves
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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Presheaf categories are well-known to be varieties of algebras and covarieties of coalgebras. We prove the converse: if a category is a variety as well as a covariety, then it is a presheaf category. Our main result is that all coalgebras on a set functor H form a presheaf category iff H is a reduction of a polynomial functor.