2026/07/29 by Francesco Dagnino, Jacopo Emmenegger, Andrea Giusto
Computer Science · Mathematics · #cs.LO #math.CT
arxiv created 2026/07/29 · arxiv updated 2026/07/30
Jacobs comprehension categories subsume a large class of categorical models of type dependency, supporting also the description of morphisms between types. We study the relationship between comprehension categories and a particular subclass, which we call Lawvere-Ehrhard comprehension categories. First, we characterize this subclass by comparing a fibration of terms and a fibration of type morphisms associated to a given comprehension category. Next, we provide the construction of the free comprehension category over a fibration. Finally, we construct the free Lawvere-Ehrhard comprehension category over a Jacobs comprehension category.