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On the other hand, the theory of triangulated categories is simpler than the theory of stable ∞-categories or dg-categories, and in many applications the triangulated structure is sufficient. An example is the proof of the Bloch–Kato conjecture , where many computations were done at the level of triangulated categories, and the additional ...
If C has products, then given an isomorphism: the mapping :, composed with the canonical map : of symmetry, is a partial involution.; If C is a triangulated category, the Karoubi envelope Split(C) can be endowed with the structure of a triangulated category such that the canonical functor C → Split(C) becomes a triangulated functor.
Printable version; In other projects ... Pages in category "Employment classifications" The following 75 pages are in this category, out of 75 total. This list may ...
It is convention to assume the category is essentially small, so that the collection of all stability conditions on forms a set (). In good circumstances, for example when D = D b Coh ( X ) {\displaystyle {\mathcal {D}}={\mathcal {D}}^{b}\operatorname {Coh} (X)} is the derived category of coherent sheaves on a complex manifold X ...
In the branch of mathematics called homological algebra, a t-structure is a way to axiomatize the properties of an abelian subcategory of a derived category.A t-structure on consists of two subcategories (,) of a triangulated category or stable infinity category which abstract the idea of complexes whose cohomology vanishes in positive, respectively negative, degrees.
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Triangulated category