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generator (Definition)

Definition 0.1. Let us consider an abelian category 𝒞. Then, an object G of 𝒞 is called a generator if Hom𝒞(G,A) is nonzero for every nonzero object A of 𝒞.


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See Also: compactness lemma

Keywords:  generator of an abelian category, cogenerator

Cross-references: abelian category
There are 24 references to this object.

This is version 2 of generator, born on 2009-06-15, modified 2009-06-15.
Object id is 801, canonical name is Generator.
Accessed 2110 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
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