English

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

R2 v1 2026-06-23T14:36:05.230Z