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)

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (next): $\S 6.1$