Abstract
We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory. Then we define categories with families formally in Martin-Löf's intensional intuitionistic type theory. Finally, we discuss the coherence problem for these internal categories with families.
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© 1996 Springer-Verlag Berlin Heidelberg
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Dybjer, P. (1996). Internal type theory. In: Berardi, S., Coppo, M. (eds) Types for Proofs and Programs. TYPES 1995. Lecture Notes in Computer Science, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61780-9_66
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DOI: https://doi.org/10.1007/3-540-61780-9_66
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