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compact object (Definition)

Let us consider an additive category $\mathcal{A}$ with arbitrary direct sums (also called coproducts).

Definition 0.1   An object $X$ of $\mathcal{A}$ is called compact if, for an arbitrary set of objects of $\mathcal{A}$ and a morphism

$\displaystyle f : X \to \bigoplus_{\alpha \in I} M_{\alpha},$
there exists some finite set $S \subset I$ such that $Im ~f$ is a subobject of $\alpha \in \bigoplus_{\alpha \in S} M_{\alpha}.$



"compact object" is owned by bci1.

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See Also: compactness lemma

Also defines:  coproduct
Keywords:  compact, Abelian category

Cross-references: morphism, object, additive category
There are 6 references to this object.

This is version 4 of compact object, born on 2009-06-15, modified 2009-06-15.
Object id is 802, canonical name is CompactObject.
Accessed 743 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 )
Pending Errata and Addenda
None.
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