/sci/ - Science & Math

Can someone motivate the definition of a morphism of varieties? I understand that regular functions on each open set are meant to pull back to regular functions on the preimage of that open set, but what information or underlying structure is this meant to capture? Even the degree of a variety isn’t invariant up to isomorphism, so what will even be the same about two isomorphic varieties?
I feel like I’m also not really asking the right questions about this so if you have anything to add that I didn’t really ask about feel free to explain.
Thanks a bunch

>>12167119
/thread and based