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 functions 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.

Not really related

Last revised on July 2, 2017 at 09:18:52. See the history of this page for a list of all contributions to it.