… triangulated category admitting small coproducts. The foundation of our approach is a
construction of local cohomology functors on triangulated categories, … a triangulated category that …

… cohomological functor on a triangulated category induces a functor between certain categories
of determinant functors… of determinant functors on triangulated categories, but we would …

… we will fall back on the homology functor H : Dh(A) -» A. The form our theorem will take is
quite general. Starting with any abelian category .4, one can construct a rather curious …

… cohomology theories through Edgar Brown's theorem [6,7]. More generally, one can form
analogous triangulated categories over the homotopical category … functor between h-categories …

… Let S be a triangulated category with a good metric. Suppose we are given a fully faithful
triangulated functor F : S ⟶ T ; we consider also the functor Y : T ⟶ Mod – S , which takes an …

… by formally inverting the suspension functor; it is equivalent … homotopy category, so it is a
topological triangulated category … as a triangulated category, to the homology category of some …

… of DG R-modules whose cohomology vanishes in positive and negative degree, respectively.
… triangulated category with set indexed coproducts. We shall denote the suspension functor …

… In K-theory for triangulated categories II we will prove … to wait until Ktheory for triangulated
categories III. Conceptually, the … It is the bottom homology of Xpo, placed in degree 0. From …

… Using this support, we study the behavior of the local cohomology functors and show that
these triangulated functors respect boundedness. Then we restrict our study to the categories …

… To see this, note that the cohomology functor hk on D(R) is … This functor preserves both
coproducts and products (… triangulated category. They are needed as tools in sections 5 and 6. …