Coproduct (Category Theory)

In category theory, a coproduct is a colimit of the following diagram:

$$AB$$ $$\text{require}AMScd\begin{array}{ccccc}A& \stackrel{i_1}{\to }& A+B& \stackrel{i_2}{\leftarrow }& B\end{array}\pi$$

Remarks

In the category of categories, the coproduct of $\mathcal{C}$ and $\mathcal{D}$ is a category $\mathcal{C}+\mathcal{D}$ with

• objects being the disjoint union of the sets of objects.
• morphisms being the projection of the morphisms from $\mathcal{C}$, and $\mathcal{D}$.