Modal Predicates and Co-equations

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.

• Type: Journal
• Year: 2002
• Where: ENTCS
• Authors: Alexander Kurz, Jirí Rosický
• Keywords: ENTCS 2002, Equations, General Base Category, Special Case