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In category theory, a branch of mathematics, a stable ∞-category is an ∞-category such that *(i) It has a zero object. *(ii) Every morphism in it admits a fiber and cofiber. *(iii) A triangle in it is a fiber sequence if and only if it is a cofiber sequence. The homotopy category of a stable ∞-category is triangulated. A stable ∞-category admits finite limits and colimits. Examples: the derived category of an abelian category and the ∞-category of spectra are both stable. A stabilization of an ∞-category ''C'' having finite limits and base point is a functor from the stable ∞-category ''S'' to ''C''. It preserves limit. The objects in the image have the structure of infinite loop spaces; whence, the notion is a generalization of the corresponding notion (stabilization (topology)) in classical algebraic topology. By definition, the t-structure of an stable ∞-category is the t-structure of its homotopy category. Let ''C'' be a stable ∞-category with a t-structure. Then every filtered object in ''C'' gives rise to a spectral sequence , which, under some conditions, converges to By the Dold–Kan correspondence, this generalizes the construction of the spectral sequence associated to a filtered chain complex of abelian groups. == Notes == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stable ∞-category」の詳細全文を読む スポンサード リンク
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