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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∈SMα.


"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
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 2572 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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