# What is the coproduct in the category of commutative rings? [closed]

My question: What is the coproduct in the category of commutative rings?

• With or without unity?
– user239203
Sep 10 '19 at 21:57

I will assume that you require your rings to be unital. Then the coproduct will just be the tensor product over $$\mathbb{Z}$$, i.e. the tensor product as $$\mathbb{Z}$$-modules (or equivalently abelian groups) with the induced ring structure.