What is "coproduct"

n. 1 Any of multiple products that are produced at the same time, or by the same process 2 (context mathematics English) A structure constructed from several similar structures, equipped with appropriate (l/en inclusion map inclusion maps), which generalises the (l/en: disjoint union) of sets, of topological spaces and the (l/en: free product) of groups

In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is the category-theoretic dual notion to the categorical product, which means the definition is the same as the product but with all arrows reversed. Despite this seemingly innocuous change in the name and notation, coproducts can be and typically are dramatically different from products.