Category theory MOC

Cocartesian category

A cocartesian category is a (necessarily symmetric) monoidal category whose tensor product is a coproduct and whose tensor unit is an initial object. #m/def/cat Specifically for any 𝐴,𝐵 ∈𝖢, there exist natural transformations

so that the data

satisfy the universal property of the coproduct.

From a finitary coproduct category

By the dual result, any category 𝖢 with chosen finite coproducts gives rise to a cocartesian category.

See also

• The dual concept is Cartesian category.
• A Bicartesian category is both of these simultaneously.

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