Weight structures and the algebraic $K$-theory of stable $\infty$-categories

Abstract

We introduce the notion of a bounded weight structure on a stable $\infty$-category and use this to prove the natural generalization of Waldhausen's sphere theorem: We show that the algebraic $K$-theory of a stable $\infty$-category with a bounded non-degenerate weight structure is equivalent to the algebraic $K$-theory of the heart of the weight structure.

Now includes relation to other recent results; improved exposition and clarity in the corollaries of the main theorem

References in corpus (1)

• Higher Topos Theory

Cited by in corpus (5)

• Categorical Milnor squares and K-theory of algebraic stacks
• Stable moduli spaces of hermitian forms
• On nilpotent extensions of $\infty$-categories and the cyclotomic trace
• A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras
• A dévissage theorem of non-connective $K$-theory