\({K_i}\)-group of \(t\)-structure of triangulated category. (Chinese. English summary) Zbl 1463.18010
Summary: Based on the properties of \(t\)-structure of a triangulated category, the paper discusses the relationship between the \({K_i}\)-groups of \(t\)-structure of the triangulated category and \({K_i}\)-groups of the triangulated category. Moreover, if \(t\)-structure is stable, it is shown that \({K_i}\)-group of triangulated category is isomorphic to the direct sum of \({K_i}\)-groups of \(t\)-structure.
MSC:
18F25 | Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) |
18G80 | Derived categories, triangulated categories |