universal coefficient theorem

theorem that homology with integer coefficients completely determines homology and cohomology with any Abelian group as coefficients
Intangible theorem Q2495664
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universal coefficient theorem

Summary

universal coefficient theorem is a theorem[1]. It draws 333 Wikipedia views per month (theorem category, ranking #177 of 1,306).[2]

Key Facts

  • universal coefficient theorem's instance of is recorded as theorem[3].
  • universal coefficient theorem is a type of theorem[4].
  • universal coefficient theorem is part of list of theorems[5].
  • universal coefficient theorem's proved by is recorded as Eduard Čech[6].
  • universal coefficient theorem's proved by is recorded as Samuel Eilenberg[7].
  • universal coefficient theorem's proved by is recorded as Saunders Mac Lane[8].
  • universal coefficient theorem's studied by is recorded as category theory[9].
  • universal coefficient theorem's maintained by WikiProject is recorded as WikiProject Mathematics[10].

Body

Definition and Type

universal coefficient theorem's instance of is recorded as theorem[3]. It is a type of theorem[4].

Use and Application

universal coefficient theorem is part of list of theorems[5].

Why It Matters

universal coefficient theorem draws 333 Wikipedia views per month (theorem category, ranking #177 of 1,306).[2] It has Wikipedia articles in 8 language editions, a strong signal of global cultural recognition.[11]

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APA 4ort.xyz Knowledge Graph. (2026). universal coefficient theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/universal-coefficient-theorem
MLA “universal coefficient theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/universal-coefficient-theorem.
BibTeX @misc{4ortxyz_universal-coefficient-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{universal coefficient theorem}}, year = {2026}, url = {https://4ort.xyz/entity/universal-coefficient-theorem}, note = {Accessed: 2026-05-03}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 6w ago · Charp238 · 2026-05-25 view diff on Wikidata ↗
    Part of
    Part of list of theorems
    Instance of theorem
    Subclass of
    + 8 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P2534]]: \begin{aligned}0\to H_{i}(X,\mathbb {Z} )\otimes A\,{\overset {\mu }{\to }}\,H_{i}(X,A)\to \operatorname {Tor} _{1}(H_{i-1}(X,\mathbb {Z} ),A)\to 0\\ 0"
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