NettetIf C is stable, one defines a triangulated structure on its homotopy category D = h o C by demanding that its exact triangles are precisely those arising from fiber sequences. Then we see immediately that (1)- (3) imply (h1)- (h3). That is, we have a map from "oo-categorical" t-structures on C to t-structures on h o C. NettetIn algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory.Every such cohomology theory is representable, as follows from Brown's representability theorem.This means that, given a cohomology theory:, there exist spaces such that evaluating the cohomology theory in degree on a space is …
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NettetLet modA be the category of finitely generated right A-modules over an artin algebra ⋀, and F be an additive subfunctor of . Let P(F) denote the full sucategory of A with … http://www.tac.mta.ca/tac/volumes/30/52/30-52.pdf dual light hubbell
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NettetTriangulated categories De nition 1.1. A triangulated category is an additive category C equipped with an additive self-equivalence and a class of distinguished ... TR3. … NettetIn particular, if the suspension functor is an equivalence, then Cis a triangulated category. A left triangulated category (C;;/) can be de ned dually, with : C!C being … NettetTriangulated categories 3 ring elements f 1,f 2 there existed a unique element ffactoring them as f 1 =fι 1 and f 2 =fι 2. (ii) Let Rbe a ring (associative, with unit element).Then the category R- Mod of all R-modules is additive.Similarly, the category R-mod of finitely generated R-modules is additive.In particular, the categories Ab of abelian groups and … dual light christmas trees