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 $\mathcal{C}$ [2]).

Bibliography

1

Ref. $[266]$ in the Bibliography for categories and algebraic topology

2

Ref. $[288]$ in the Bibliography for categories and algebraic topology