Work

The category of π-finite spaces

Year: 2025

Type: article

Abstract: We show that the category of truncated spaces with finite homotopy invariants ( π -finite spaces) has many of the features expected of an elementary ∞-topos. It should be thought of as the natural higher analogue of the elementary 1-topos of finite sets, with which it shares several initiality properties. The paper has also an appendix about univalent families in ∞-pretopoi.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2025.107925

Author: Mathieu Anel

Institution: Carnegie Mellon University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Air Force Office of Scientific Research