Cofinality Theorems of Infinity Categories and Algebraic K-Theory
Algebraic Topology
2024-05-07 v1 K-Theory and Homology
Abstract
In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application demonstrates that cofinal full inclusion functors of (\infty)-categories are weak homotopy equivalences. For our second application, we provide an alternative proof of Barwick's cofinality theorem of algebraic (K)-theory.
Keywords
Cite
@article{arxiv.2405.03498,
title = {Cofinality Theorems of Infinity Categories and Algebraic K-Theory},
author = {Hisato Matsukawa},
journal= {arXiv preprint arXiv:2405.03498},
year = {2024}
}