Yes, you might be right, this might be completely clear, and I just find it confusing for some reason but from the example in the OP I have no idea the point it

Yes, you might be right, this might be completely clear, and I just find it confusing for some reason but from the example in the OP I have no idea the point it is trying to get across with these terms, e.g: """ This is covariance in action: Every bike is a vehicle. (But not every vehicle is a bike.) Every bike factory is a vehicle factory. (But not every vehicle factory is a bike factory.) """ As far as for tensor stuff, I think what is confusing to me at least, is that the components of standard vectors are contravariant, while their dual covectors are covariant. contravariant tensors raise indices and covariants lower them. Anyway I'm glad this is clear to you but I find it confusing. Although I wonder now if there is a mapping from the OO diagrams in the OP with Penrose Tensor notations where everything will just make sense.... edit: missing word