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arXiv · 2607.27170

Free constructions for comprehension categories

Francesco Dagnino·Jacopo Emmenegger·Andrea Giusto
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Abstract

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.

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Francesco Dagnino, Jacopo Emmenegger, Andrea Giusto. 2026-07-29. Free constructions for comprehension categories. https://arxiv.org/abs/2607.27170

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