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I've tried searching the web for information on how to construct the coproduct in the category of (noncommutative) algebras over a ring. I know that in the commutative case it is the tensor product, but I've been told that there exists a general construction as well, akin to the free product of groups (at least in some cases).

Can anyone help me with this?

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# Coproduct in the category of algebras

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