We can take a derivative of a container with respect to an isolated object \(p_0 \colon P s\). The shapes in the derivative are pairs of objects \( (s \colon S, p_0 \colon P s ) \) and the positions are functors to \(P s \textbackslash p_0 \) (the category \(P s\) with the (isolated) object \(p_0\) removed).

One can even define container optics:
\[ O\langle a, b \rangle \langle s, t \rangle = \int^{S \triangleleft P} (s \to T_{S \triangleleft P} a) \times (T_{S \triangleleft P} b \to t) \]

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