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Categorical Universal Coalgebra
A Case Study
Algebraic and Coalgebraic Specifications
A Categorical Notions
B Basic Notions of Modal Logic
arrow base category bStr called category of coalgebras category theory chapter characterise closure co-Birkhoff coalgebra morphisms coalgebraic logic cocongruences codomain coequalisers cofree coalgebra cointersections colimits commutes comonad consider coreflection morphism corollary covariety creates factorisations denoted diagram dualise endofunctor equalisers equational logic example factorisation structure factorisation system fibration fibred final coalgebra follows forgetful functor full subcategory functor on Set generalised given Gumm and Schroder hence Herrlich hidden signature implies infinitary injective isomorphic kernel pair Kripke frames Kripke models largest behavioural equivalence largest bisimulation left adjoint logic for coalgebras M-coreflective M)-category M)-factorisation mapping modal logic modally definable Moreover multiplicative functor notion objects preserves weak pullbacks propositional variables pushouts quotients reflective subcategory Remark right adjoint Rutten S)-structures semantics Setn signature for coalgebras small coproducts split epi Strong Mono structure for sinks subcoalgebras subsystems universal coalgebra variety theorem