# Mapping/Composition/Definition

Composition

Let and denote sets, let

and

be mappings. Then the mapping

is called the * composition* of the mappings
and .

Composition

Let ${}L,\,M$ and ${}N$ denote sets, let

- $F\colon L\longrightarrow M,x\longmapsto F(x),$

and

- $G\colon M\longrightarrow N,y\longmapsto G(y),$

be mappings. Then the mapping

- $G\circ F\colon L\longrightarrow N,x\longmapsto G(F(x)),$

is called the * composition* of the mappings
${}F$ and ${}G$.