▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
Map composition operation
Formulation 0
Let $X$, $Y$, and $Z$ each be a D11: Set such that
(i) $Y^X$, $Z^Y$, and $Z^X$ are each a D68: Set of maps
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}