Corpus ID: 54093785

Localization in Homotopy Type Theory

@article{Christensen2018LocalizationIH,
  title={Localization in Homotopy Type Theory},
  author={J. D. Christensen and Morgan Opie and E. Rijke and Luis Scoccola},
  journal={arXiv: Algebraic Topology},
  year={2018}
}

J. D. Christensen, Morgan Opie, +1 author Luis Scoccola

Published 2018

Mathematics

arXiv: Algebraic Topology

We study localization at a prime in homotopy type theory, using self maps of the circle. Our main result is that for a pointed, simply connected type $X$, the natural map $X \to X_{(p)}$ induces algebraic localizations on all homotopy groups. In order to prove this, we further develop the theory of reflective subuniverses. In particular, we show that for any reflective subuniverse $L$, the subuniverse of $L$-separated types is again a reflective subuniverse, which we call $L'$. Furthermore, we… CONTINUE READING

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