Corpus ID: 221507831

Internal $\infty$-Categorical Models of Dependent Type Theory: Towards 2LTT Eating HoTT

  title={Internal \$\infty\$-Categorical Models of Dependent Type Theory: Towards 2LTT Eating HoTT},
  author={Nicolai Kraus},
Using dependent type theory to formalise the syntax of dependent type theory is a very active topic of study and goes under the name of “type theory eating itself” or “type theory in type theory.” Most approaches are at least loosely based on Dybjer’s categories with families (CwF’s) and come with a type Con of contexts, a type family Ty indexed over it modelling types, and so on. This works well in versions of type theory where the principle of unique identity proofs (UIP) holds. In homotopy… Expand

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