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Question for the mathematical audience

  • April 20th, 2006

I have now been staring at this particular sentence for way too long, and thus will start using any and all communication lines I can find to get assistance. Either I’m being way too stupid, or the author neglects to mention some salient detail.

Setup: \phi\colon G^\prime\to G is a group homomorphism, A\in kG-\operator{mod}, A^\prime\in kG^\prime-\operator{mod}. A can be given the structure of a kG^\prime-module by pulling back through \phi, i.e. we define g^\prime a:=\phi(g^\prime)a for g^\prime\in G^\prime and a\in A.

So far it’s all crystal clear for me. However, it then turns out that we’re highly interested in using a morphism f\in\operator{Hom}_G(A,A^\prime) and I cannot for the life of me find out how such beasts are guaranteed to exist. If it where f\in\operator{Hom}_{G^\prime}(A,A^\prime), I wouldn’t have any problems with it; but then the stuff I need/want to do with it don’t work out.

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Michi is a recent PhD working in homological algebra and applied algebraic topology. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
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