  We introduce a notion of differential of a Sobolev map between metric spaces.
The differential is given in the framework of tangent and cotangent modules of
metric measure spaces, developed by the first author. We prove that our notion
is consistent with Kirchheim's metric differential when the source is a
Euclidean space, and with the abstract differential provided by the first
author when the target is $\mathbb{R}$.

Functional Analysis