Using the word "AFTER" as a preposition of place

[NeeSoo]

Could you please explain for me how the word "AFTER" can be as a preposition of place???
I found that we use it when one follows the other.
e.g: " The cat ran after the dog"
Can we consider it in this way as a preposition of place?? and why????

[Jamie (K)]

I think you can think of it as a preposition of place, because "after" indicates that the cat is behind the dog. Their position keeps moving, but "after" still indicates the cat's place relative to the dog.