Smart answer:
Your search for ′What is the counterpart to injective maps′ returned the following results:
surjective maps
The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map G
Source:
the monomorphisms
The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.
Source: