direct limit
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English
[edit]Noun
[edit]direct limit (plural direct limits)
- (algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If in the indexing poset, then there exist and . If such that then . If k = j then .)
- A direct limit has “canonical functions” which map each element of the disjoint union to its equivalence class.
- Direct limits in the algebraic sense are models of category-theoretic colimits.
- (category theory) a colimit