ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
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▼ Zermelo-Fraenkel set theory
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▼ Binary relation
▼ Map
▼ Identity map
Definition D4428
Canonical identity map
Formulation 0
A D18: Map $f : X \to Y$ is a canonical identity map on $X$ if and only if
(1) \begin{equation} \forall \, x \in X : f(x) = x \end{equation} (D440: Identity map)
(2) \begin{equation} X = Y \end{equation}