| dbo:abstract |
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 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 in classical algebraic topology. By definition, the t-structure of a 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. (en) |
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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 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. (en) |
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Stable ∞-category (en) |
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freebase:Stable ∞-category wikidata:Stable ∞-category https://global.dbpedia.org/id/f77A |
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wikipedia-en:Stable_∞-category?oldid=999695445&ns=0 |
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wikipedia-en:Stable_∞-category |
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