compact object

(Definition)

Let us consider an additive category 𝒜 with arbitrary direct sums (also called coproducts).

Definition 0.1. An object X of 𝒜 is called compact if, for an arbitrary set of objects of 𝒜 and a morphism

⊕ f : X → M α, α∈I

there exists some finite set S ⊂ I such that Im f is a subobject of α ∈⊕ _α∈SM_α.

"compact object" is owned by bci1.
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See Also: compactness lemma

Also defines:

coproduct

Keywords:

compact, Abelian category

Cross-references: additive category
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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 2653 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 )

compact object

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