left inverse

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Noun

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 : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s \circ f = \mbox{id}_X .

Antonyms

• right inverse

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