Standard Lemma guide

morphism

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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  • Received-Pronunciation: /ˈmɔːfɪzəm/
  • General-American: /ˈmɔɹfɪzəm/
  • US: Recorded audio is listed in the source snapshot.
  • rhymes with -ɔː(ɹ)fɪzəm

1

noun

Meaning 1

(formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.

Definition source: English Wiktionary via Wiktextract

Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences

Examples

  • 1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50, 1° The composition of two morphisms is defined if and only if the final object of the first morphism is the initial object of the second. This composition is also a morphism, whose initial object is the initial object of the first morphism and whose final object is the final object of the second.
  • 1992, Terrance Brown (translator), Gil Henriques, Chapter 13: Morphisms and Transformations in the Construction of Invariants, Terrance Brown (translator), Jean Piaget, Gil Henriques, Edgar Ascher (editors), Morphisms and Categories: Comparing and Transforming, page 198, In certain extreme cases in mathematics, the synthesis of morphisms and of transformations is so intimate that one can speak of a veritable fusion. [...] Essentially, categories are sets of morphisms organized into operatory systems.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

Being or having distinct variants of a plant or animal species in the same locale; polymorphism.

Definition source: English Wiktionary via Wiktextract

Topics: biology, natural-sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Generalised from isomorphism, etc.

Across languages

Translations

25 source translations are retained for this English entry.

  • Bashkir: морфизм (morfizm) — arrow in a category
  • Bulgarian: морфизъм (morfizǎm) — arrow in a category
  • Chinese Mandarin: 態射 /态射 (tàishè) — arrow in a category
  • Czech: morfismus — arrow in a category
  • Danish: morfi — arrow in a category
  • Dutch: morfisme — arrow in a category
  • Finnish: morfismi — arrow in a category
  • Finnish: nuoli — arrow in a category
  • French: morphisme — arrow in a category
  • German: Morphismus — arrow in a category
  • Icelandic: mótun — arrow in a category
  • Italian: morfismo — arrow in a category
  • Japanese: 型射 (keisha) — arrow in a category
  • Japanese: 射 (sha) — arrow in a category
  • Kazakh: морфизм (morfizm) — arrow in a category
  • Korean: 사상 (sasang) — arrow in a category
  • Kyrgyz: морфизм (morfizm) — arrow in a category
  • Latin: morphismus — arrow in a category
  • Persian: ریخت — arrow in a category
  • Polish: morfizm — arrow in a category
  • Portuguese: morfismo — arrow in a category
  • Russian: морфизм (morfizm) — arrow in a category
  • Spanish: morfismo — arrow in a category
  • Ukrainian: морфізм (morfizm) — arrow in a category
  • Welsh: morffedd — arrow in a category