Smooth and Proper Maps with Respect to a Fibration

Authors

Mathieu Anel, Carnegie Mellon University
Jonathan Weinberger, Chapman UniversityFollow

Document Type

Article

Publication Date

11-6-2024

Abstract

This paper explain how the geometric notions of local contractibility and properness are related to the Σ-types and Π-types constructors of dependent type theory. We shall see how every Grothendieck fibration comes canonically with such a pair of notions—called smooth and proper maps—and how this recovers the previous examples and many more. This paper uses category theory to reveal a common structure between geometry and logic, with the hope that the parallel will be beneficial to both fields. The style is mostly expository, and the main results are proved in external references.

Comments

This article was originally published in Mathematical Structures in Computer Science in 2024. https://doi.org/10.1017/S096012952400032X

Recommended Citation

Anel, M., & Weinberger, J. (2024). Smooth and proper maps with respect to a fibration. Mathematical Structures in Computer Science, 1–14. https://doi.org/10.1017/S096012952400032X

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.