PlanetPhysics/C 3Category

Abelian C₃-category

Let $𝒜$ 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 $𝒜$ 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 $𝒜b5$-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.