functor

in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)
Thing general Q864475
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functor

Summary

functor ranks in the top 2% of general entities by monthly Wikipedia readership (369 views/month).[1]

Key Facts

  • functor is credited with the discovery of Samuel Eilenberg[2].
  • functor is credited with the discovery of Saunders Mac Lane[3].
  • functor's image is recorded as Commutative diagram of a functor.svg[4].
  • functor's subclass of is recorded as function[5].
  • functor's part of is recorded as category theory[6].
  • functor's Commons category is recorded as Functors[7].
  • functor's Freebase ID is recorded as /m/02yzn[8].
  • functor's topic's main category is recorded as Category:Functors[9].
  • functor's PSH ID is recorded as 7364[10].
  • functor's OmegaWiki Defined Meaning is recorded as 955376[11].
  • functor's Encyclopædia Britannica Online ID is recorded as topic/functor[12].
  • functor's different from is recorded as function object[13].
  • functor's properties for this type is recorded as P1568[14].
  • functor's properties for this type is recorded as P1571[15].
  • functor's defining formula is recorded as \begin{aligned}F(\operatorname{id}X)&=\operatorname{id}{F(X)}\F(f\circ g)&=Ff\circ Fg\end{aligned}[16].
  • functor's studied by is recorded as category theory[17].
  • functor's MathWorld ID is recorded as Functor[18].
  • functor's Treccani ID is recorded as funtore[19].
  • functor's Quora topic ID is recorded as Functor-1[20].
  • functor's JSTOR topic ID is recorded as functors[21].
  • functor's nLab ID is recorded as functor[22].
  • functor's maintained by WikiProject is recorded as WikiProject Mathematics[23].
  • functor's Microsoft Academic ID is recorded as 156772000[24].
  • functor's ProofWiki ID is recorded as Definition:Functor[25].
  • functor's in defining formula is recorded as F[26].

Body

Works and Contributions

Credited discoveries include Samuel Eilenberg[2], a mathematician[27], 1913–1998[28], of Poland[29], awarded the Guggenheim Fellowship[30], specialised in topology[31] and Saunders Mac Lane[3], a mathematician[32], 1909–2005[33], of United States[34], awarded the Guggenheim Fellowship[35], specialised in algebra[36].

Why It Matters

functor ranks in the top 2% of general entities by monthly Wikipedia readership (369 views/month).[1] functor has Wikipedia articles in 23 language editions, a strong signal of global cultural recognition.[37] functor is known by 30 alternative names across languages and contexts.[38]

References

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

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [2] . History of Homological Algebra. wikidata.org.
  3. [3] . History of Homological Algebra. wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . Freebase Data Dumps. 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] . Quora. wikidata.org.
  20. [21] . wikidata.org.
  21. [22] . wikidata.org.
  22. [23] . wikidata.org.
  23. [24] . wikidata.org.
  24. [25] . wikidata.org.
  25. [26] . wikidata.org.

Inline context (facts about related entities)

  1. [27] . Wikidata. wikidata.org. → on this site
  2. [28] . Wikidata. wikidata.org. → on this site
  3. [29] . Wikidata. wikidata.org. → on this site
  4. [30] . Wikidata. wikidata.org. → on this site
  5. [31] . Wikidata. wikidata.org. → on this site
  6. [32] . Wikidata. wikidata.org. → on this site
  7. [33] . Wikidata. wikidata.org. → on this site
  8. [34] . Wikidata. wikidata.org. → on this site
  9. [35] . Wikidata. wikidata.org. → on this site
  10. [36] . Wikidata. wikidata.org. → on this site

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [37] . Wikidata sitelinks. wikidata.org.
  3. [38] . 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). functor. Retrieved April 10, 2026, from https://4ort.xyz/entity/functor
MLA “functor.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/functor.
BibTeX @misc{4ortxyz_functor_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{functor}}, year = {2026}, url = {https://4ort.xyz/entity/functor}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): functor — https://4ort.xyz/entity/functor (retrieved 2026-04-10)

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