This is a formalization of the results described in the paper "Non-accessible localizations" available at my web page. A link to a talk is also available at that page.

Here is a mapping between the results in the paper and the formalization. Some results from Smallness.v in this repo have been merged upstream into the Coq-HoTT library; these are indicated with Universes.Smallness below.

Proposition 2.2:          Smallness.issmall_n_image
Lemma 2.3:                Universes.Smallness.islocallysmall_trunc
Lemma 2.4:                Smallness.islocallysmall_truncmap
Lemma 2.5:                Smallness.issmall_truncmap_connected
Theorem 2.6:              Smallness.issmall_iff_islocallysmall_truncated
Theorem 2.6 (2nd proof):  Smallness.issmall_iff_islocallysmall_truncated'
Corollary 2.7:            Smallness.issmall_truncmap_issmall_truncation
Remark 2.9:               Universes.Smallness.issmall_inhabited_issmall
Proposition 3.2:          NonAccessible.restrict_O
Theorem 3.3:              NonAccessible.nonaccessible_localization

You will likely need to edit the _CoqProject file to make this build on your system.

Also, the universe variables are sensitive to the library version (and maybe the Coq version):

• Commit 61d56b17 from March 13, 2025 builds with Coq 8.20.1 and Coq-HoTT library version dd2ca5cb from March 11, 2025.

• Commit e6cf3466 from September 26, 2024 builds with Coq 8.19.1 and Coq-HoTT library version b0082605 from Sep 26, 2024. Some parts of the file Smallness.v have now been merged into Coq-HoTT in Universes/Smallness.v.

• Commit 0bed3109 from February 3, 2024 builds with Coq 8.18.0 and Coq-HoTT library version fc8e5b46 from February 6, 2024.

• Commit 9015e6d0 from January 1, 2024 builds with Coq 8.18.0 and Coq-HoTT library version 698ca2fb from January 1, 2024.

• Commit 9943c0a2 from September 29, 2023 builds with Coq 8.18.0 and Coq-HoTT library version a3bde181 from September 27, 2023.

• Commit 1b8e486b from February 26, 2023 builds with Coq 8.16.1 and Coq-HoTT library version 8d1c6a7e from February 26, 2023.

• Commit 33ee3baf from June 6, 2022 builds with Coq 8.15.1 and Coq-HoTT library version bca7ccfa from May 23, 2022.