Category theory MOC

Cocartesian category

A cocartesian category is a monoidal category whose tensor product is a coproduct and whose tensor unit is an initial object. cat Specifically for any 𝐴,𝐵 ∈𝖢, there exist natural transformations

𝜆𝐵:1⇒1⊗𝐵:𝖢→𝖢𝜌𝐴:1⇒𝐴⊗1:𝖢→𝖢

so that the data

(𝐴⊗𝐵,𝜆𝐵𝐴,𝜌𝐴𝐵)

satisfy the universal property of the coproduct.

See also

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

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