Small object arguments, plus-construction, and left-exact localizations
Category Theory
2020-04-14 v2
Abstract
We present a variant of the small object argument, inspired by Kelly, better suited to construct unique factorisation systems. Our main result is to compare it to the plus-construction involved in sheafification. We apply this to construct localizations, modalities and left-exact localizations explicitly from generators.
Cite
@article{arxiv.2004.00731,
title = {Small object arguments, plus-construction, and left-exact localizations},
author = {Mathieu Anel and Chaitanya Leena Subramaniam},
journal= {arXiv preprint arXiv:2004.00731},
year = {2020}
}
Comments
v2. Add a couple of examples