nLab
inverse function

Given sets AA and BB and a function f:ABf\colon A \to B, the inverse function of ff (if it exists) if the function f 1:BAf^{-1}\colon B \to A such that both composite function?s ff 1f \circ f^{-1} and f 1ff^{-1} \circ f are identity functions. Note that ff has an inverse function if and only if ff is a bijection, in which case this inverse function is unique.

Inverse functions are inverse morphisms in the category Set of sets.

More generally, in any concrete category, the inverse of any isomorphism is given by the inverse of the corresponding function between underlying sets.

Created on July 20, 2012 01:40:58 by Toby Bartels (75.88.84.217)