Biproduct (Category Theory)

Definition

A category $\mathcal{C}$ has biproducts whenever products and coproducts coincide:

$$\prod _{i:I}{X}_i\cong \coprod _{i:I}{X}_i\forall (I,X):\mathrm{Fam}(\mathcal{C})$$

Like with products and coproducts, we say:

• $\mathcal{C}$ has binary biproducts whenever $I\cong 2$.
• $\mathcal{C}$ has finite biproducts whenever $|I|<{\aleph }_0$.
• $\mathcal{C}$ has small biproducts whenever $I$.

References

maclane1978-categories