Let $\Omega$ be a type (or signature, depending on your terminology), and let $\mathbf {\Omega Alg}$ be the category of $\Omega$-algebras. What is the coproduct in this category?
G. Bergman's "An invitation to general algebra and universal constructions" hints at this, but (unless I am overlooking something, it's a big book) doesn't provide an explicit construction for it. Where can I find an explicit construction of it? It should be noncommutative, nonassociative, etc. etc.