Abstract and concrete categories
Abstract and concrete categories
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
On the greatest fixed point of a set functor
Theoretical Computer Science
A small final coalgebra theorem
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Automata and Algebras in Categories
Automata and Algebras in Categories
Infinite trees and completely iterative theories: a coalgebraic view
Theoretical Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
Theoretical Computer Science - Logic, semantics and theory of programming
A comonadic account of behavioural covarieties of coalgebras
Mathematical Structures in Computer Science
The intersection of algebra and coalgebra
Theoretical Computer Science - Algebra and coalgebra in computer science
Algebra ∩ coalgebra = presheaves
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Covarieties of coalgebras: comonads and coequations
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
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A concept of equation morphism is introduced for every endofuctor $F$ of a cocomplete category $\Ce$. Equationally defined classes of $F$-algebras for which free algebras exist are called varieties. Every variety is proved to be monadic over $\Ce$, and, conversely, every monadic category is equivalent to a variety. The Birkhoff Variety Theorem is also proved for $`{\sf Set}\hbox{-like}'$ categories.By dualising, we arrive at a concept of coequation such that covarieties, that is, coequationally specified classes of coalgebras with cofree objects, correspond precisely to comonadic categories. Natural examples of covarieties are presented.