Abstract
AbstractThis paper continues a series of papers that develop a new approach to syntax and semantics of dependent type theories. Here we study the interpretation of the rules of the identity types in the intensional Martin-Löf type theories on the C-systems that arise from universe categories. In the first part of the paper we develop constructions that produce interpretations of these rules from certain structures on universe categories while in the second we study the functoriality of these constructions with respect to functors of universe categories. The results of the first part of the paper play a crucial role in the construction of the univalent model of type theory in simplicial sets.
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. S. Awodey and M. A. Warren, Homotopy theoretic models of identity types, Math. Proc. Camb. Philos. Soc., 146 (2009), 45–55.
2. LIPIcs;M. Bezem,2013
3. J. Cartmell, Generalised algebraic theories and contextual categories, Ph.D. Thesis, Oxford University, 1978. See http://www.cs.ru.nl/~spitters/Cartmell.pdf.
4. J. Cartmell, Generalised algebraic theories and contextual categories, Ann. Pure Appl. Log., 32 (1986), 209–243.
5. Lecture Notes in Comput. Sci.;P. Dybjer,1996