[[Category theory MOC]]
# Bicartesian category

A [[monoidal category]] is called **bicartesian** iff its tensor product is a [[biproduct]] and its tensor unit is a zero object (both initial and terminal). #m/def/cat
Thus it is both [[Cartesian category|cartesian]] and [[Cocartesian category|cocartesian]] with a certain compatibility condition.

## Examples

- [[Category of left modules]] under the [[Direct sum of modules]].

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