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Glite Dictionary
homomorphism

homomorphism

1 9.9
A rule that links two math systems and keeps how you combine elements the same
  • noun
  • /ˌhoʊməˈmɔrfɪzəm/
  • Specialized
translation icon : homomorfismo
  • A homomorphism is a mapping that preserves the algebraic structure between two groups.

Examples

  • This is good news because parallel programming folks understand list homomorphisms pretty well.

    Blog text (17)

  • So ring homomorphisms and ideals congruence in Z.

  • And if you have a group homomorphism and it's onto.

  • So if a graph homomorphism inequality.

  • What about the number of homomorphisms from a triangle to G?

  • What is the probability that a generically chosen payoff function is a homomorphism contains information about that structure?

  • Sawzall is entirely based on list homomorphisms.

    Blog text (17)

  • Using the Artin map, we might induce homomorphisms...

    Sneakers (1992)

  • There must be a one-to-one homomorphism, a little math lingo, so that each vote can be connected to one registered legal voter, and vice versa.

    Blog text (1)

  • The concept of homomorphism is crucial in understanding how different algebraic structures relate to each other.

Synonyms

morphism
vshomomorphism
  • Specialized
9.9

A function between mathematical objects that keeps their structure

is used across mathematical structures rather than mainly in category theory

Surface Forms

homomorphism singular
homomorphisms plural

Morphology

homomorphism = morphism (semi-transparent) = homo + morphism

The elements 'homo-' ('same') and 'morphism' (a structure-preserving map) are analyzable, but the full technical meaning requires mathematical background.

Etymology

Homomorphism comes from the Greek parts homo- meaning 'same' and -morph meaning 'form'. So a homomorphism is a function that connects two math structures while keeping the important 'form' and the way their parts work together.