For this question, there were originally a few questions in mind, but now just this one. I particularly want to get more feedback of PS part.
- I refer to this. But I really want to have a better understanding the part highlighted, which explains why the case is not faithful, by using the example of affine map and automorphism.
PS: For category of ring, are there many morphisms K-algebra ring mapping itself, sending to the identity morphism of units group? Why there are many morphisms rather than one? Since automorphisms are all elements map to themselves?
definition of units ring: A ring with $1_{R}$ with multiplicative inverse elements. Why it is only an identity map?
What's the difference of mapping between the first category and the second one? I hope I explain my question clearly.
BTW: Downvoted does not help. Punishing rather than educating is meaningless.
Please let me know if you have any question about what I ask. Greatly appreciate your contribution here.