Word.ws English Dictionary

direct limit

direct limit noun: 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 i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.).

Noun

direct limit (plural direct limits)

  1. 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 i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.)
    • 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.
    Synonyms:
    inductive limit
  2. a colimit

Synonyms of direct limit

  • inductive limit

Antonyms

Forms of direct limit

pluraldirect limits

Questions about direct limit

What does direct limit mean?
Direct limit means 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 i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.).
What part of speech is direct limit?
Direct limit is a noun.
What is the plural of direct limit?
The plural of direct limit is direct limits.

Words near direct limit in the dictionary

  1. direct initiative
  2. direct initiatives
  3. direct intent
  4. direct intents
  5. direct inward dialing
  6. direct limit
  7. direct limits
  8. direct mail
  9. direct marketing
  10. direct maternal death
  11. direct maternal deaths

Source and license

Adapted from Wiktionary: direct limit (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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