diff --git a/_data/seminar.yml b/_data/seminar.yml index 3a6e971ba8a1ed3bbe38cd1514f8763e00c2156c..dc2a1453ecf43ecc4a96da2c6afe4ab2f54be1e9 100644 --- a/_data/seminar.yml +++ b/_data/seminar.yml @@ -26,7 +26,7 @@ speaker: Niyousha Najmaei picture: https://niyoushanajmaei.github.io/images/nioosha.png website: https://niyoushanajmaei.github.io/ - lab: IRIF + lab: LIX title: A Type Theory for Comprehension Categories with Applications to Subtyping abstract: | We develop a type theory that we show is an internal language for comprehension categories. This type theory is closely related to Martin-Löf type theory (MLTT). Indeed, semantics of MLTT are often given in comprehension categories, albeit usually only in discrete or full ones. As we explain, requiring a comprehension category to be full or discrete can be understood as removing one “dimension” of morphisms. Thus, in our syntax, we recover this extra dimension. We show that this extra dimension can be used to encode subtyping in a natural way. Important instances of non-full comprehension categories include ones used for constructive or univalent intensional models of MLTT and directed type theory, and so our syntax is a more faithful internal language for these than is MLTT.