arXiv Open Access 2024

On internally projective sheaves of groups

David Wärn

Lihat Sumber

Abstrak

A sheaf of modules on a site is said to be internally projective if sheaf hom with the module preserves epimorphism. In this note, we give an example showing that internally projective sheaves of abelian groups are not in general stable under base change to a slice. This shows that internal projectivity is weaker than projectivity in the internal logic of the topos, as expressed for example in terms of Shulman's stack semantics. The sheaf of groups that we use as a counterexample comes from recent work by Clausen and Scholze on light condensed sets.

Topik & Kata Kunci

math.CT

Penulis (1)

David Wärn

Format Sitasi

APA MLA BibTeX

Wärn, D. (2024). On internally projective sheaves of groups. https://arxiv.org/abs/2409.12835

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓