TITLE: Is the category of commutative group schemes abelian?
QUESTION [23 upvotes]: I think, because in the category of schemes, all finite limits exist, the commutative group
objects with homomorphisms should form an abelian category. 
Is this true? And do you know anywhere to cite this?

REPLY [2 votes]: should be not true! What is the cokernel of the map $\mathbb{Z}\rightarrow A$ with $A$ an abelian variety and $\mathbb{Z}$ the constant group scheme represented by the ring of integers?  But if you consider only commutative algebraic group scheme over a field $k$(i.e. of finite type over $k$), then it should be abelian.