Definition:Evaluation Mapping

Definition
Let $S, T$ be sets, and let $S^T$ be the set of all mappings from $T$ to $S$.

The evaluation mapping for $S^T$ is the mapping $\operatorname{ev}: S^T \times T \to S$ defined by:


 * $\map {\operatorname{ev} } {f, t} := \map f t$

Also known as
Various other notations for $\operatorname{ev}$ exist, in particular $\operatorname{eval}$ and $\epsilon$.

Also see

 * Definition:Exponential (Category Theory)