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If there exists a homomorphism $f: A \rightarrow B$ between two groups $A$ and $B$, and a homomorphism $g: C \rightarrow D$ between two groups $C$ and $D$, then will there exist a homomorphism $h: A*C \rightarrow B*D$ between the free products $A*C$ and $B*D$?

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    What are the conditions on $h$, with regards to $f$ and $g$? Maybe take a look at http://en.wikipedia.org/wiki/Coproduct, since the free product is the coproduct in the category of groups you might find your answer there.2011-03-21
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    @shamovic: you should post this as an answer, so it can be accepted and upvoted :D2011-03-21
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    I would, but I'm not sure it is the one h988h looks for. So I want some clarification.2011-03-21

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