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