Equivariant Sheaves and Functors
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Cites background or methods from "Equivariant Sheaves and Functors"
...Similarly, if A = (AX, Ā, β) ∈ D K(X) is an element of the equivariant derived category, then ([BL] §2....
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...([BL] §2....
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...11, or by the sheaf-theoretic construction of [BL] §5....
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...In this section we recall the construction [BL] and some of the basic properties of the equivariant derived category of sheaves of vectorspaces over the real numbers R (although these constructions work more generally for sheaves of modules over any ring of finite cohomological dimension....
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...[BL] §12....
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Cites background from "Equivariant Sheaves and Functors"
...categories C, D is a pair (F, νF) consisting of a functor F : C −→ D and a natural isomorphism νF : F ◦[ 1 ]C ∼= [1]D◦F (here [1]C,[1]D are the translation functors) with the property that exact triangles in C are mapped to exact triangles in D. The appropriate equivalence relation between such functors is ‘graded natural isomorphism’ which means natural isomorphism compatible with the maps νF [4, section 1]. Ignoring set-theoretic ......
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...Hom∗(E, F) ⊗C E // F // TE(F) [ 1 ] hh...
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...The grading is such that if one ignores the differential, TE(F) = F ⊕ (hom(E, F) ⊗ E)[ 1 ]....
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...categories C, D is a pair (F, νF) consisting of a functor F : C −→ D and a natural isomorphism νF : F ◦[1]C ∼= [1]D◦F (here [ 1 ]C,[1]D are the translation functors) with the property that exact triangles in C are mapped to exact triangles in D. The appropriate equivalence relation between such functors is ‘graded natural isomorphism’ which means natural isomorphism compatible with the maps νF [4, section 1]. Ignoring set-theoretic ......
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...By a curve in (D,�) we mean a subset c ⊂ D \ ∂D which can be represented as the image of a smooth embedding γ : [0; 1 ] −→ D such that γ−1(�) = {0;1}....
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