(i) | $Y^X$, $Z^Y$, and $Z^X$ are each a D68: Set of maps |

**composition operation**on $Z^Y \times Y^X$ is the D3489: Operation \begin{equation} Z^Y \times Y^X \to Z^X, \quad (f, g) \mapsto (x \mapsto f(g(x))) \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

Formulation 0

Let $X$, $Y$, and $Z$ each be a D11: Set such that

The **composition operation** on $Z^Y \times Y^X$ is the D3489: Operation
\begin{equation}
Z^Y \times Y^X \to Z^X, \quad
(f, g) \mapsto (x \mapsto f(g(x)))
\end{equation}

(i) | $Y^X$, $Z^Y$, and $Z^X$ are each a D68: Set of maps |