Dimension is a functor. This is true for points in space as well as arrays (more concretely).

Consider a point in $$\mathbb{R}$$. Then $$x \mapsto (x, 0)$$ is a map $$\mathbb{R} \rightarrow \mathbb{R}^2$$; $$F_f(x) = (f(x), 0)$$. One can imagine many such functors adding two dimensions, etc.

In J, looping is characteristically idiosyncratic: one lifts verbs with the aid of the " conjunction.

This iteration applying functions resembles functors in Haskell:

fmap :: Functor f => (a -> b) -> f a -> f b

i.e. " gives us a family of functors, indexed by integers.