Reassembling datatypes from functors using a fixed-point

Iowa Type Theory Commute

Last episode we discussed how functors can describe a single level of a datatype. In this episode, we discuss how to put these functors back together into a datatype, using disjoint unions of functors and a fixed-point datatype. The latter expresses the idea that inductive data is built in any finite number of layers, where each layer is described by the functor for the datatype.