Weight structures and the algebraic $K$-theory of stable $\infty$-categories
K-Theory and Homology
2019-11-19 v2 Algebraic Topology
Category Theory
Abstract
We introduce the notion of a bounded weight structure on a stable -category and use this to prove the natural generalization of Waldhausen's sphere theorem: We show that the algebraic -theory of a stable -category with a bounded non-degenerate weight structure is equivalent to the algebraic -theory of the heart of the weight structure.
Keywords
Cite
@article{arxiv.1812.09751,
title = {Weight structures and the algebraic $K$-theory of stable $\infty$-categories},
author = {Ernest E. Fontes},
journal= {arXiv preprint arXiv:1812.09751},
year = {2019}
}
Comments
Now includes relation to other recent results; improved exposition and clarity in the corollaries of the main theorem