---- > [!definition] Definition. ([[categorical biproduct]]) > Let $\mathsf{C}$ be a [[category]] with [[terminal object|zero object]]. The **biproduct** of a finite collection of objects in $\mathsf{C}$ is an object that is both the [[categorical product|product]] and [[categorical coproduct|coproduct]] of those objects. ^definition > [!basicexample] > The canonical example comes from the [[category]] $\mathsf{Ab}$ of [[abelian group|abelian groups]], cf. [[finite direct products and coproducts align in the category of abelian groups]]. Many examples are then built upon this one, e.g. [[direct sum of modules]], [[TVS direct sum|topological direct sums]], even [[direct sum of sheaves of modules]]. ^basic-example ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```