Translation guide
The concept of isomorphism—a structural correspondence between two systems—is expressed in Japanese primarily through the technical term 同型 (どうけい) in mathematics and computer science, and 異種同形 (いしゅどうけい) in biology. For general or metaphorical use, descriptive phrases are more natural.
A one-to-one structure-preserving mapping between two sets or systems.
Standard technical term for isomorphism in mathematics, logic, and computer science. Often used in compounds like 同型写像 (isomorphism mapping).
この二つの群は同型である。
These two groups are isomorphic.
Sometimes used interchangeably with 同型, but can also mean 'same shape' in non-technical contexts. In mathematics, 同型 is preferred for abstract structure, while 同形 may emphasize literal shape.
グラフの同形性を判定する。
Determine the isomorphism of graphs.
Specifically 'isomorphism mapping' or 'isomorphism map', used when emphasizing the function itself.
同型写像を構成する。
Construct an isomorphism mapping.
Similarity in form or structure between different species or organisms.
Biological term for isomorphism, referring to structural similarity between different species.
これらの生物は異種同形を示している。
These organisms exhibit isomorphism.
Can be used in biology to mean 'same form', but less specific than 異種同形. Context clarifies whether it refers to mathematical or biological isomorphism.
同形の器官が異なる種に見られる。
Isomorphic organs are found in different species.
A structural parallel or correspondence between different domains, systems, or ideas.
There is no single natural Japanese word for metaphorical isomorphism. Instead, use phrases like 構造的に対応している (structurally correspond) or 同じ構造を持つ (have the same structure).
この二つの理論は構造的に対応している。
These two theories are isomorphic.
両者の間には同型性が見られる。
An isomorphism can be seen between the two.
Noun meaning 'isomorphism' as a property. Can be used in broader intellectual contexts, but still sounds somewhat technical.
文化の同型性について議論する。
Discuss the isomorphism of cultures.
Directly translating 'isomorphism' as 同型 outside of technical contexts can sound unnatural or overly academic. In everyday language, rephrase to describe the structural similarity.