left inverse

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English

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Noun

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left inverse (plural left inverses)

  1. (mathematics) A related function that, given the output of the original function, returns the input that produced that output.
    In order for a function to have a left inverse it must be injective.
  2. (category theory) For a given morphism f : XY, its right inverse (if it has one) is a morphism s : YX such that .

Usage notes

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Given two functions and , is the left inverse of iff for all in , . The term is only used if there exists a in such that , and an unqualified inverse is preferred if no such exists.

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