PlanetPhysics/C 3Category

Abelian C3-category
Let $$\mathcal{A}$$ be an Abelian cocomplete category, defined as the dual of an Abelian complete category.

A $$C_3$$-category is defined as a cocomplete Abelian category $$\mathcal{A}$$ such that the following distributivity relation holds for any direct family $$\left\{A_i\right\}$$ and any subobject $$B$$:

$$(\bigcup A_i) \bigcap B = \bigcup (A_i \bigcap B),$$ 

A $$C_3$$-category is also called an $$\mathcal{A}b5$$-category.

The dual of the Cartesian closed category of finite Abelian quantum groups with exponential elements (including Lie groups) and quantum group homomorphisms is a $$C_3$$-category.