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$C_1$-category

(Definition)

Definition 0.1. A category 𝒞1 with coproducts is called a C1-category if for every family of of monomorphisms {u : A → B } i i i the morphism

ι := ⊕iui : ⊕i Ai → ⊕i Bi

is also a monomorphism ([1]).

Remark 0.1. With certain additional conditions (as explained in ref. [1]) 𝒞1 may satisfy the Grothendieck axiom 𝒜b5, thus becoming a C3-category (Ch. 11 in [1]).

References

[1]   See p.81 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: Grothendieck category, $C_3$-category

Other names:  C1-category
Also defines:  C1-category
Keywords:  categories, Ab5 categories

Cross-references: monomorphisms, coproducts, category

This is version 5 of $C_1$-category, born on 2010-05-09, modified 2010-05-09.
Object id is 855, canonical name is C_1Category2.
Accessed 3209 times total.

Classification:
Physics Classification: 00. (GENERAL)

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