$C_3$-category

Definition 0.1   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$ :

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

([1])

Remark 0.1  

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

Example 0.1   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.

Bibliography

1
See p.82 and eq. (1) in ref. $ [266]$ in the Bibliography for categories and algebraic topology

2
Ref. $ [288]$ in the Bibliography for categories and algebraic topology



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