What is "left inverse"

n. 1 (context mathematics English) A related function that, given the output of the original function returns the input that produced that output. 2 (context category theory English) For a given morphism ''f'' : ''X'' → ''Y'', its ''right inverse'' (if it has one) is a morphism ''s'' : ''Y'' → ''X'' such that $s\; circ\; f\; =\; mbox\{id\}\_X$.

A left inverse in mathematics may refer to:

• A left inverse element with respect to a binary operation on a set
• A left inverse function for a mapping between sets
• A kind of generalized inverse