---
type: "concept"
title: "Composition of maps"
slug: "composition-of-maps"
language: "en"
translationGroupId: "cmrezsrcy0007qh01ts3fyd63"
domain: "Logic"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

Given maps $f:X \rightarrow Y$ and $g:Y \rightarrow Z$, their composite $g\circ f:X \rightarrow Z$ is the map defined by
$$(g\circ f)(x)=g(f(x))\quad\text{for all }x\in X.$$