Categories with Dependence and Semantics of Dependent Types
Abstract
The present paper gives a generalization of cartesian closed categories, called cartesian closed categories with dependence, whose strict version induces categories with families that support 1-, Sigma- and Pi-types in the strict sense. Consequently, we have obtained a new semantics of dependent type theories that is both categorical and true-to-syntax.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2017
- DOI:
- 10.48550/arXiv.1704.04747
- arXiv:
- arXiv:1704.04747
- Bibcode:
- 2017arXiv170404747Y
- Keywords:
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- Mathematics - Category Theory;
- Computer Science - Logic in Computer Science