surjective maps

The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map .

In the dual point of view to a surjection of sheaves

In the dual point of view, an injective map corresponds to a surjection of sheaves, and a surjective map corresponds to an injection of sheaves.

surjective

In other words, the induced map is surjective.

g : :} A → P ( A ) {\displaystyle gA\to {\mathcal {P}}(A)} defined by x ↦ { x } {\displaystyle x\mapsto \{x\

On the other hand, g : A → P ( A ) {\displaystyle g:A\to {\mathcal {P}}(A)} defined by x ↦ { x } {\displaystyle x\mapsto \{x\}} is an injective map.