$C_3$-category | Physics Library

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. in the Bibliography for categories and algebraic topology
2: Ref. in the Bibliography for categories and algebraic topology

-category" is owned by bci1.
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