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arXiv · 1812.09751

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

Ernest E. Fontes
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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.

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Ernest E. Fontes. 2018-12-23. Weight structures and the algebraic $K$-theory of stable $\infty$-categories. https://arxiv.org/abs/1812.09751

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