Suppose S is a family of L-structures where L is some collection of constant symbols, relation symbols, and function symbols. Does the coproduct of elements of S exist? If not, how does one prove it? If yes, how is the coproduct defined? Are the maps from elements of S to the coproduct all monic? If you are aware of references related to this question, I would be happy to know them. Thanks in advance for your comments.