PlanetPhysics/C2 Category

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In general, a $C_2$-category  is an $𝒜b4$-category, or, alternatively, an $𝒜b3$- and $𝒜b{3}^{*}$ -category $ℂ$ with certain additional conditions for the canonical [[../TrivialGroupoid/|morphism]] from direct sums to products of any family of [[../TrivialGroupoid/|objects]] in $𝒞$ ).

A $C_2$-category is defined as a [[../Cod/|category]] $𝒞$ that has products, [[../Coproduct/|coproducts]] and a zero object, and if the morphism $\iota :\oplus A_i\to 𝐗A_i$ is a [[../InjectiveMap/|monomorphism]] for any family of objects $\left\{A_i\right\}$ in $𝒞$ (p. 81 in ).

One readily obtains the result that a $C_2$-category is $C_1$ ().