PlanetPhysics/C2 Category

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In general, a $C_{2}$-category  is an ${\mathcal {A}}b4$-category, or, alternatively, an ${\mathcal {A}}b3$- and ${\mathcal {A}}b3^{*}$ -category $\mathbb {C}$ with certain additional conditions for the canonical morphism from direct sums to products of any family of objects in ${\mathcal {C}}$ ).

A $C_{2}$-category is defined as a category ${\mathcal {C}}$ that has products, coproducts and a zero object, and if the morphism $\iota :\oplus A_{i}\to \mathbf {X} A_{i}$ is a monomorphism for any family of objects $\left\{A_{i}\right\}$ in ${\mathcal {C}}$ (p. 81 in ).

One readily obtains the result that a $C_{2}$-category is $C_{1}$ ().