The category of $\pi$-finite spaces
Category Theory
2025-03-05 v4 Algebraic Topology
Abstract
We show that the category of truncated spaces with finite homotopy invariants (\=/finite spaces) has many of the features expected of an elementary \oo 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 \oo pretopoi.
Keywords
Cite
@article{arxiv.2107.02082,
title = {The category of $\pi$-finite spaces},
author = {Mathieu Anel},
journal= {arXiv preprint arXiv:2107.02082},
year = {2025}
}
Comments
v2. add an initiality result and the proof that not all pushout exist. v3 new appendix on univalent families in pretopoi and renew section on the universe of pi-finite spaces, corrected a few mistakes. v4 simplified a few proofs, last version before publication in JPAA