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 $$\C$$ 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 $$C_1$$.