Theorem of the heart in negative K-theory for weight structures

الأصل · EN

We construct the strong weight complex functor (in the sense of Bondarko) for a stable infinity-category C equipped with a bounded weight structure w. Along the way we prove that C is determined by the infinity-categorical heart of w. This allows us to compare the K-theory of C and the K-theory of Hw, the classical heart of w. In particular, we prove that Kₙ(C) → Kₙ(Hw) are isomorphisms for n ≤ 0.