Modal Predicates and Coequations

Alexander Kurz, Jiří Rosický
2002 Electronical Notes in Theoretical Computer Science  
We show how coalgebras can be presented by operations and equations. This is a special case of Linton's approach to algebras over a general base category X , namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.
doi:10.1016/s1571-0661(04)80364-5 fatcat:44m54cet3vaitf3g27szekzvt4