4 ms·
A natural transformation between endofunctors? How exactly? That's just a family of functions µ : F(x) -> G(x) such that for all (f : x -> y), (F(f);µ ==
by tel 11y ago
A natural transformation between endofunctors? How exactly? That's just a family of functions
µ : F(x) -> G(x)
such that for all (f : x -> y), (F(f);µ == µ;G(f)). I don't see how that's capturing anything interesting here. If µ were a natural isomorphism with inverse µ- then there'd be laws like (F(f) == µ;G(f);µ-), but this exactly involves introducing an inverse so the natural transformation didn't buy much.
- AdieuToLogic 11y agoI thought of endofunctors due to morphisms remaining in the same domain (satisfying the homogeneous domain/codomain requirement of natural transformations), though perhaps a better description would have been to constrain the functors to injective arrows instead.