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Unformatted text preview: G 1 G 2 G n solvable? (7) If f : A B is an equivalence in a category C and g : B A is a morphism such that gf = 1 A and fg = 1 B , show that g is unique. (8) (a) Prove that any two universal (initial) objects in a category C are equivalent. (b) Prove that any two couniversal (terminal) objects in a category C are equivalent. (9) In the category of abelian groups, show that the group A 1 A 2 together with the homomorphisms 1 : A 1 A 1 A 2 , 1 ( x ) = ( x,e ) 2 : A 2 A 1 A 2 , 2 ( x ) = ( e,x ) is a coproduct for { A 1 ,A 2 } . Why is this not a coproduct in the category of groups?...
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 Fall '08
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 Algebra

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