Modal Predicates and Coequations
Alexander Kurz, Jiřı́ Rosický · Electronic Notes in Theoretical Computer Science · 2002
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.