Unformatted text preview: Problem 19.3. A ∆ﬁltered object M is projective iﬀ Ext 1 ( M, ∆( E )) = 0 for all E . Problem 19.4. (1) Show that the double centralizer property is equivalent to Ext 1 ( M,P ) = for any projective P and M ∈ O tor . (2) Use the naive duality to show that π is fully faithful on injectives. (3) Show that π has left adjoint π ! and that π ◦ π ! is the identity on the image of π . 1 This exercise and the next problem also appeared last time. 1...
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 Fall '12
 IvanLosev
 Math, Algebra, Vector Space, Limit, Functor, Adjoint functors, Natural Transformation, SYMPLECTIC REFLECTION ALGEBRAS

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