  Many algorithms in numerical analysis are affine equivariant: they are immune
to changes of affine coordinates. This is because those algorithms are defined
using affine invariant constructions. There is, however, a crucial ingredient
missing: most algorithms are in fact defined regardless of the underlying
dimension. As a result, they are also invariant with respect to non-invertible
affine transformation from spaces of different dimensions. We formulate this
property precisely: these algorithms fall short of being natural
transformations between affine functors. We give a precise definition of what
we call a weak natural transformation between functors, and illustrate the
point using examples coming from numerical analysis, in particular B-Series.
