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$C_2$-category

(Definition)

In general, a C2-category is an 𝒜b4-category, or, alternatively, an 𝒜b3- and 𝒜b3∗ -category C∗ with certain additional conditions for the canonical morphism from direct sums to products of any family of objects in 𝒞 [2]).

Definition 0.1. A C2-category is defined as a category 𝒞 that has products, coproducts and a zero object, and if the morphism ι : ⊕Ai → XAi is a monomorphism for any family of objects {Ai } in 𝒞 (p. 81 in [1]).

Remark 0.1. One readily obtains the result that a C2-category is C1 ([1]).

References

[1]   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: Grothendieck category

Also defines:  $C_2$-category
Keywords:  Grothendieck category

Cross-references: monomorphism, coproducts, category
There is 1 reference to this object.

This is version 4 of $C_2$-category, born on 2010-05-09, modified 2010-05-09.
Object id is 853, canonical name is C2Category.
Accessed 2717 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )

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