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$C_3$-category (Definition)
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



"$C_3$-category" is owned by bci1.

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See Also: $C_1$-category, Grothendieck category

Other names:  C3-category
Also defines:  $C_3$-category
Keywords:  C3-category, $C_3$-category, Grothendieck category

Cross-references: homomorphisms, Lie groups, quantum groups, relation, cocomplete Abelian category, category
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This is version 1 of $C_3$-category, born on 2010-05-09.
Object id is 856, canonical name is C_3Category.
Accessed 589 times total.

Classification:
Physics Classification: 00. (GENERAL)
Pending Errata and Addenda
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