Category theory for computing science
Category theory for computing science
Handbook of logic in computer science (vol. 1)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Equational and implicational classes of coalgebras
Theoretical Computer Science
Covarieties and complete covarieties
Theoretical Computer Science
Equational axiomatizability for coalgebra
Theoretical Computer Science
Modal logic
What is the coalgebraic analogue of Birkhoff's variety theorem?
Theoretical Computer Science
A Completeness result for equational deduction in coalgebraic specification
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Mongruences and Cofree Coalgebras
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
A comonadic account of behavioural covarieties of coalgebras
Mathematical Structures in Computer Science
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Covarieties of coalgebras: comonads and coequations
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
| Hi-index | 0.00 |
We present the dual to Birkhoff's variety theorem in terms of predicates over the carrier of a cofree coalgebra (that is, in terms of ‘coequations’). We then discuss the dual to Birkhoff's completeness theorem, showing how closure under deductive rules dualises to yield two modal operators acting on coequations. We discuss the properties of these operators and show that they commute. We prove as our main result the invariance theorem, which is the formal dual of Birkhoff's completeness theorem.