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Math Help - Category

  1. #1
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    How can I see that the functor


    <br /> <br />
A \mapsto A \otimes_{\mathbb Z} A<br />
    from the category of abelian groups to itself is not additive.
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  2. #2
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    Quote Originally Posted by peteryellow View Post
    How can I see that the functor

    <br /> <br />
A \mapsto A \otimes_{\mathbb Z} A<br />
    from the category of abelian groups to itself is not additive.
    if it was additive, then we'd have: f(x) \otimes g(y) + g(x) \otimes f(y) = 0, for all x,y \in G_1, all abelian groups G_1, G_2, and all f, g \in \text{Hom}_{\mathbb{Z}}(G_1,G_2). but this is nonsense! (consider trivial examples!)
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