Categorical structures for type theory in univalent foundations

@article{Ahrens2018CategoricalSF,
  title={Categorical structures for type theory in univalent foundations},
  author={B. Ahrens and P. Lumsdaine and V. Voevodsky},
  journal={ArXiv},
  year={2018},
  volume={abs/1705.04310}
}
  • B. Ahrens, P. Lumsdaine, V. Voevodsky
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in univalent type theory, where the comparisons between them can be given more elementarily than in set-theoretic foundations. Specifically, we construct maps between the various types of structures, and show that assuming the Univalence axiom, some of the… CONTINUE READING
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