English

Smooth and Proper Maps

Category Theory 2025-02-14 v5 Logic in Computer Science Algebraic Geometry Logic

Abstract

This is an expository note explaining how the geometric notions of local connectedness and properness are related to the Σ\Sigma-type and Π\Pi-type constructors of dependent type theory.

Keywords

Cite

@article{arxiv.2402.00331,
  title  = {Smooth and Proper Maps},
  author = {Mathieu Anel and Jonathan Weinberger},
  journal= {arXiv preprint arXiv:2402.00331},
  year   = {2025}
}

Comments

Dedicated to Andr\'e Joyal to his 80th birthday; 13 pages, 4 tables. v2 simplified Table 3 and corrected the characterization of acyclic/localic maps in the corresponding examples. v3 add more examples. v4 final version before publication, change title, update bibliography. v5 corrected Def. 2.2.1. of the published version. Updated affiliation