Corpus ID: 118647868

A type theory for cartesian closed bicategories

  title={A type theory for cartesian closed bicategories},
  author={Marcelo P. Fiore and Philip Saville},
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal property, thereby lifting the Curry-Howard-Lambek correspondence to the bicategorical setting. Our approach is principled and practical. Weak substitution structure is constructed using a bicategorification of the notion of abstract clone from universal algebra, and… Expand
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A type theory for cartesian closed bicategories (Extended Abstract)
  • M. Fiore, P. Saville
  • Computer Science
  • 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
  • 2019
This work introduces a type theory modelling the structure of a cartesian closed bicategory and shows that its syntactic model satisfies an appropriate universal property, thereby lifting the Curry-Howard-Lambek correspondence to the bicategorical setting. Expand
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