English

Calculus of Fractions for Quasicategories

Algebraic Topology 2025-08-19 v2 Combinatorics Category Theory

Abstract

We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove that the marked Ex-functor can be used to compute the localization of a marked quasicategory satisfying our condition and that the appropriate (co)completeness properties of the quasicategory carry over to its localization.

Keywords

Cite

@article{arxiv.2306.02218,
  title  = {Calculus of Fractions for Quasicategories},
  author = {Daniel Carranza and Chris Kapulkin and Zachery Lindsey},
  journal= {arXiv preprint arXiv:2306.02218},
  year   = {2025}
}

Comments

57 pages, v2 removed application and appendix, added new results