Do you think Rick actually cares for Morty?

Knowing all that he knows about the universe, I think that he can't help it but behave cynically towards any human being (even himself, see his kill count with the council of Ricks).
But given his standards, I'd say he actually cares for Morty. The room where he stores all of Morty's traumatic memories is proof of how much time and effort he's willing to give for one Morty given that there are thousands of them.

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