noun
morphism
MOR-fiz-um
Morphism (noun) means a structure-preserving map from one mathematical object to another, treated in category theory as an arrow between objects. Example: “In category theory, every morphism has a source and a target.”
noun
1
technical A structure-preserving map from one mathematical object to another, treated in category theory as an arrow between objects.
"In category theory, every morphism has a source and a target."
"Two morphisms can be composed when the target of the first is the source of the second."
"A morphism between two groups is usually a homomorphism."
How to use morphism
Learner’s notesIn plain EnglishA mathematical arrow that carries one object to another while keeping its structure.
When to use it
It is a technical term used almost entirely in mathematics.
Memory tip
Think of a morphism as a function-like arrow whose exact meaning depends on the kind of object involved.
Trace the full origin ↓
Common pairings
morphism of groups
composition of morphisms
identity morphism
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In category theory, every _____ has a source and a target.
Etymology
Generalised from terms such as isomorphism.
Synonyms
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Rhymes for morphism
See all rhymes for morphism →Frequently asked questions
What is a morphism in maths?
A morphism is an arrow between two objects in a category. Informally, it is a map from one mathematical object to another that preserves structure.
What is the difference between a morphism and a homomorphism?
The two words are largely interchangeable. Morphism is used almost exclusively in category theory, while homomorphism is more common in algebra.
How do you pronounce morphism?
In British English it is said roughly MOR-fiz-um, with the stress on the first syllable.
What is the meaning of morphism?
"morphism" (noun) means a structure-preserving map from one mathematical object to another, treated in category theory as an arrow between objects.
