About: Stable ∞-category

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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.

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rdfs:label	Stable ∞-category (en)
rdfs:comment	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)
dcterms:subject	Higher category theory
Wikipage page ID	42081371 (xsd:integer)
Wikipage revision ID	999695445 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic topology Derived category Morphism Limit (category theory) Zero object Spectrum (topology) Triangulated category Dold–Kan correspondence Higher category theory Abelian category Abelian group Homotopy category Spectral sequence Category theory Chain complex T-structure Fiber sequence ∞-category Cofiber sequence Colimit dbr:Glossary_of_infinity_category dbr:Stabilization_(topology)
sameAs	Stable ∞-category Stable ∞-category Stable ∞-category
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Category_theory dbt:Categorytheory-stub dbt:Lurie-HA
has 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)
prov:wasDerivedFrom	wikipedia-en:Stable_∞-category?oldid=999695445&ns=0
page length (characters) of wiki page	1917 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stable_∞-category
is Link from a Wikipage to another Wikipage of	Derived algebraic geometry Glossary of category theory Compact object (mathematics) Active users Triangulated category K-theory of a category Module spectrum Stable infinity category Stabilization (category theory)
is Wikipage redirect of	Stable infinity category Stabilization (category theory)
is foaf:primaryTopic of	wikipedia-en:Stable_∞-category

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