English

Towards constructivising the Freyd-Mitchell embedding theorem

Category Theory 2022-03-24 v1 Logic

Abstract

The aim of the paper is to first point out that the classical proof of the Freyd-Mitchell Embedding Theorem does not work in CZF; then, to propose an alternative embedding of a small abelian category into the category of sheaves of modules over a ringed space, which works constructively. It is necessary to mention that this work has been initially inspired by Erik Palmgren, who unexpectedly passed away in November 2019: I'm very grateful to him for having shared with me his intuitions, and for having supervised the realization of the first half of the paper.

Cite

@article{arxiv.2203.12490,
  title  = {Towards constructivising the Freyd-Mitchell embedding theorem},
  author = {Anna Giulia Montaruli},
  journal= {arXiv preprint arXiv:2203.12490},
  year   = {2022}
}
R2 v1 2026-06-24T10:23:31.951Z