On dependent type theory and its categorical semantics (categorical model of dependent types):
Bart Jacobs, Comprehension categories and the semantics of type dependency, Theoret. Comput. Sci. 107 2 (1993) 169-207 [MR1201808, doi:10.1016/0304-3975(93)90169-T]
Bart Jacobs, Categorical Logic and Type Theory, Studies in Logic and the Foundations of Mathematics 141, Elsevier (1998) [ISBN:978-0-444-50170-7, pdf]
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