Abstract
We present the internal type theory of a Heyting pretopos with a natural numbers object. The resulting theory is based on dependent types and proof-terms. We prove that there is a sort of equivalence between such type theories and the category of Heyting pretoposes. By using the type theory we also build the free Heyting pretopos generated by a category.
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Maietti, M.E. (1998). The internal type theory of a Heyting pretopos. In: Giménez, E., Paulin-Mohring, C. (eds) Types for Proofs and Programs. TYPES 1996. Lecture Notes in Computer Science, vol 1512. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097794
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DOI: https://doi.org/10.1007/BFb0097794
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