In 2009, Ghani, Hancock and Pattinson gave a coalgebraic characterisation of stream processors $A^mathbb{N} to B^mathbb{N}$ 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 $A^mathbb{N} to B^mathbb{N}$. Our account sites both our result and that of op. cit. within the apparatus of comodels for algebraic effects originating with Power-Shkaravska.
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