GNDT, without omega #2
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First, TT is not actually using the fact that is defined in Setω. It could just as well have been defined in, say, Set₀ and all examples would still work. Second, the definition of Map (and subsequent Fold, etc.) were highly suspicious: they were significant size changes between sources and targets. I'm not sure these are still related to the actual categorical concepts. This also manifests itself in the type of induction for LNDT, which is uselessly generalized wrt. to the Set level of `A`. Overall, having a down-to-earth definition for TT (and elsewhere) will make my life easier. (And premature universe level generalization is the root of all evil)
We can go beyond list-like containers now. This slight generalization supports any kind of sum-of-product, first-order datatype. This could be further extended to support Pi-types and Sigma-types, à la Desc described in https://www.irif.fr/~dagand/stuffs/thesis-2011-phd/thesis.pdf
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I remove the Set\omega here and there, and then deploy fold (modern version) for GNDT.