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▾ Zermelo-Fraenkel set theory
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▾ Injective map
Set of injections
Formulation 0
Let $X$ and $Y$ each be a D11: Set.
The set of injections from $X$ to $Y$ is the D11: Set \begin{equation} \mathsf{Inj}(X \to Y) : = \{ f \mid f : X \to Y \text{ is an injection} \} \end{equation}
Also known as
Set of injective maps, Set of set monomorphisms
Conventions
Convention 0 (Notation for set of injections) : Let $X$ and $Y$ each be a D11: Set. We denote the D2222: Set of injections from $X$ to $Y$ by $\mathsf{Inj}(X \to Y)$.