Definition:Translation Mapping/Affine Space

Definition
Let $\mathcal E$ and $\mathcal F$ be affine spaces.

Let $\mathcal T: \mathcal E \to \mathcal F$ be affine transformations.

Then $\mathcal T$ is a translation the tangent map $\vec {\mathcal T}$ is the identity on the tangent space $\vec {\mathcal E}$.