Stream Processors and Comodels

In 2009, Ghani, Hancock and Pattinson gave a coalgebraic characterisation of stream processors A^ℕ → B^ℕ drawing on ideas of Brouwerian constructivism. Their stream processors have an intensional character; in this paper, we give a corresponding coalgebraic characterisation of extensional stream processors, i.e., the set of continuous functions A^ℕ → B^ℕ. Our account sites both our result and that of op. cit. within the apparatus of comodels for algebraic effects originating with Power-Shkaravska.