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}
}