4 papers
AdapTT: Functoriality for Dependent Type Casts
Arthur Adjedj, Meven Lennon-Bertrand, Thibaut Benjamin +1
The ability to cast values between related types is a leitmotiv of many flavors of dependent type theory, such as observational type theories, subtyping, or cast calculi for gradua…
Beyond Eckmann-Hilton: Commutativity in Higher Categories
Thibaut Benjamin, Ioannis Markakis, Wilfred Offord +2
We show that in a weak globular -category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a h…
Naturality for higher-dimensional path types
Thibaut Benjamin, Ioannis Markakis, Wilfred Offord +2
We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a…
Generating Higher Identity Proofs in Homotopy Type Theory
Thibaut Benjamin
Finster and Mimram have defined a dependent type theory called CaTT, which describes the structure of omega-categories. Types in homotopy type theory with their higher identity typ…