Definition Let be a subset of . Then the inclusion map from to is the mapping
In other words, the inclusion map is simply a fancy way to say that every element in is also an element in .
To indicate that a mapping is an inclusion mapping, one usually writes
instead of when defining or mentioning an inclusion map. This hooked arrow symbol
can be seen as combination of the symbols and . In the above definition, we have not used this convention. However, examples of this convention would be: