• Corpus ID: 215745397

Small object arguments, plus-construction, and left-exact localizations.

@article{Anel2020SmallOA,
  title={Small object arguments, plus-construction, and left-exact localizations.},
  author={Mathieu Anel and Chaitanya Leena Subramaniam},
  journal={arXiv: Category Theory},
  year={2020}
}
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. 

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