so let's consider the natural transformation from the set-valued functor "square roots of -1" on the category of characteristic p finite fields to the terminal functor; and let's linearize the sets and then take the kernel of the natural transformation... or something like that...

so for example for p=2 we get... ??the zero functor??

while for p=3 we get... hmmm... we're taking the kernel of a non-surjective map here... ??maybe we should be using some sort of homotopy-kernel instead??