In general, a C2-category is an 𝒜b4-category, or, alternatively, an 𝒜b3- and 𝒜b3∗ -category C∗ with
certain additional conditions for the canonical morphism from direct sums to products of any
family of objects in 𝒞 [2]).
Definition 0.1. A C2-category is defined as a category 𝒞 that has products, coproducts and
a zero object, and if the morphism ι : ⊕Ai → XAi is a monomorphism for any family of
objects 
in 𝒞 (p. 81 in [1]).
Remark 0.1. One readily obtains the result that a C2-category is C1 ([1]).
References
