F-coalgebra

Summary

For an endofunctor $F$ of a category, an $F$-coalgebra is an object $A$ with a morphism $A \to F(A)$. It is the dual of an $F$-algebra. Coalgebras model state-based systems such as automata, streams and transition systems. The map describes what one can observe of a state and where it goes next. Terminal coalgebras give infinite data such as streams, and the uniqueness of maps into them gives proofs by coinduction.