Representing Nested Inductive Types Using W-Types
We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive types exist in any Martin-Löf category (extensive locally cartesian closed category with W-types) by exploiting our work on container types. This generalises a result by Dybjer (1997) who showed that non-nested strictly positive inductive types can be represented using W-types. We also provide a detailed analysis of the categorical infrastructure needed to establish the result.
KeywordsType Theory Natural Transformation Left Adjoint Elimination Rule Inductive Type
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