-category theorem

(Theorem)

Theorem 0.1. (proposition 1.2. in ref. [1].)

A cocomplete Abelian category is C₃ if and only if the direct limit of every direct family of subobjects {Ai} of an object A is equal to ⋃ A_i.

References

[1] See p.82 and eq. (1) in ref. [266] in the Bibliography for categories and algebraic topology

-category theorem" is owned by bci1.
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Other names:

Ab5 category, cocomplete Abelian category

Keywords:

cocomplete Abelian category, $C_3$

-category theorem

Attachments:: -category corollary (Corollary) by bci1
-category generators corollary (Corollary) by bci1

Cross-references: proposition
There are 2 references to this object.

This is version 2 of $C_3$

-category theorem, born on 2010-05-09, modified 2010-05-09.
Object id is 857, canonical name is C_3CategoryTheorem.
Accessed 3220 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 )

-category theorem

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