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$C_3$-category

(Definition)

Definition 0.1. Let 𝒜 be an Abelian cocomplete category, defined as the dual of an Abelian complete category.

A C3-category is defined as a cocomplete Abelian category 𝒜 such that the following distributivity relation holds for any direct family {Ai } and any subobject B:

⋃ ⋂ ⋃ ⋂ ( Ai) B = (Ai B ),

([1])

Remark 0.1.

A C3-category is also called an 𝒜b5-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 C3-category.

References

[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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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: 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 3297 times total.

Classification:
Physics Classification: 00. (GENERAL)

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