▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Structure
▾ Algebraic structure
▾ Identity element
▾ Left inverse element
▾ Left inverse map
Left-invertible map
Formulation 0
Let $f : X \to Y$ be a D18: Map.
Then $f$ is left-invertible if and only if there exists a D18: Map $g : Y \to X$ such that \begin{equation} \forall \, x \in X : g(f(x)) = x \end{equation}
Results
» R309: Left-invertible map iff injection