1. The problem statement, all variables and given/known data List all morphisms of addition for Z6 -> Z3. (integers mod 6 to integers mod 3) 2. Relevant equations Definition of morphism in text: A morphism f:(X,*) -> (X',*') is defined to be a function on X to X' which carries the operation * on X into the operation *' on X', in the sense that f(x*y)=(fx)*'(fy) for all x,y in X. A morphism of addition is where * and *' are operations of addition. 3. The attempt at a solution I've been working ahead in my class and I'm just not sure I found all the morphisms and for some reason I had trouble with this. I can do the proofs later on in the exercises though..., so I think I'm okay with the definition of a morphism... The only function that comes to mind that satisfies what was required above is f:Z6->Z3 defined by: f(x) = remainder after division by 3. I can't seem to really be certain that this is the only one though or if there are others. If it is the only one, then what if I Z3=X and Z6=X'. That is, f:Z3 -> Z6. If it isn't the only one, what approach could I employ to find it? What I did was simply write down the definition and do a few examples to see what jumped out at me to define f as. Thanks! Edit: The book hasn't covered groups yet, so I don't know. And I don't know why I didn't go through the individual options, haha. Okay, I'll try looking at it that way.