1. The problem statement, all variables and given/known data Produce an example in the category in which objects are open sets in R2 and morphisms are continuous maps, to illustrate that Hom sets need not be abelian groups in this category. 3. The attempt at a solution I'm missing something stupid here. I'd think that I was looking for two open sets A,B in R2 such that, for some f,g in Hom(A,B), fg != gf. No? I have no clue what the group operation is supposed to be.