Final Sequences and Final Coalgebras for Measurable Spaces

A measure polynomial functor is a functor in the category Meas built up from constant measurable spaces, the identity functor and using products, coproducts and the probability measure functor Δ. In [1] it was proved that these functors have final coalgebras. We present here a different proof of that fact, one that uses the final sequence of the functor, instead of an ad hoc language. We also show how this method works for certain functors in Set and explore the connection with results in the literature that use the final sequence in other ways.

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