# Definition Given a [[map]] $f: X \rightarrow Y$ and $A \subset X$, an *inclusion map* or *canonical injection* $i: A \rightarrow X$ is defined by $i(a) = a \, \forall a \in A$. Note that the right hand side here is treated as an element in $X$, i.e., the map $i$ includes elements from $A$ into $X$. They are quite simple. Inclusion maps are sometimes denoted $i: A \hookrightarrow X$. [[Identity Map|Identity maps|]] are a special case of inclusion maps.