chain complex

in homological algebra, a structure consisting of a sequence of modules and a sequence of homomorphisms between consecutive modules such that the image of each homomorphism is included in the kernel of the next
Thing general Q1143328
Press Enter · cited answer in seconds

chain complex

Summary

chain complex ranks in the top 2% of general entities by monthly Wikipedia readership (143 views/month).[1]

Key Facts

  • chain complex is credited with the discovery of Walther Mayer[2].
  • chain complex's image is recorded as Chain map.svg[3].
  • chain complex's subclass of is recorded as sequence[4].
  • chain complex's subclass of is recorded as diagram[5].
  • chain complex's Commons category is recorded as Complexes (algebra)[6].
  • chain complex's Freebase ID is recorded as /m/010wr5[7].
  • chain complex's dual to is recorded as cochain complex[8].
  • chain complex's used by is recorded as homology[9].
  • chain complex's defining formula is recorded as \begin{aligned}&\dotsb\xleftarrow{\partial_0}A_0\xleftarrow{\partial_1}A_1\xleftarrow{\partial_2}A_2\xleftarrow{\partial_3}\dotsb\&\partial_i\circ\partial_{i+1}=0\end{aligned}[10].
  • chain complex's studied by is recorded as homological algebra[11].
  • chain complex's has part is recorded as chain[12].
  • chain complex's has part is recorded as boundary operator[13].
  • chain complex's MathWorld ID is recorded as ChainComplex[14].
  • chain complex's nLab ID is recorded as chain complex[15].
  • chain complex's maintained by WikiProject is recorded as WikiProject Mathematics[16].
  • chain complex's Microsoft Academic ID is recorded as 194403031[17].
  • chain complex's ProofWiki ID is recorded as Definition:Chain_Complex[18].
  • chain complex's in defining formula is recorded as \partial_i[19].
  • chain complex's in defining formula is recorded as i[20].
  • chain complex's Namuwiki ID is recorded as 사슬 복합체[21].

Body

Works and Contributions

chain complex is credited with the discovery of Walther Mayer[2].

Why It Matters

chain complex ranks in the top 2% of general entities by monthly Wikipedia readership (143 views/month).[1] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.[22] It is known by 10 alternative names across languages and contexts.[23]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [2] . History of Homological Algebra. wikidata.org.
  3. [4] . wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . Freebase Data Dumps. wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.
  14. [15] . wikidata.org.
  15. [16] . wikidata.org.
  16. [17] . wikidata.org.
  17. [18] . wikidata.org.
  18. [19] . wikidata.org.
  19. [20] . wikidata.org.
  20. [21] . wikidata.org.

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [22] . Wikidata sitelinks. wikidata.org.
  3. [23] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). chain complex. Retrieved April 10, 2026, from https://4ort.xyz/entity/chain-complex
MLA “chain complex.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/chain-complex.
BibTeX @misc{4ortxyz_chain-complex_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{chain complex}}, year = {2026}, url = {https://4ort.xyz/entity/chain-complex}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): chain complex — https://4ort.xyz/entity/chain-complex (retrieved 2026-04-10)

Canonical URL: https://4ort.xyz/entity/chain-complex · Last refreshed: