The set of maps from $A$ to $B$[1] is the set $\textup{Hom}_{\mathsf{Sets}}\webleft (A,B\webright )$[2] whose elements are the functions from $A$ to $B$.


Footnotes

[1] Further Terminology: Also called the Hom set from $A$ to $B$.
[2] Further Notation: Also written $\mathsf{Sets}\webleft (A,B\webright )$.

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