can i connect my ps4 to macbook pro and how?

What exactly are you wanting to do that you'd need to "connect" them? If you want to transfer files between the two, use a USB thumb drive or external drive.

I have a similar problem.. I understand that my mbp (late 2013) does not have a HDMI input therefore i cannot plug in the (ps4) hdmi to my mbp and play.

If anyone can help me with specifics as to what additional component i would need to purchase to enable me to use my mbp screen to play the ps4 if i do not wish to purchase a gaming monitor or a tv. Any help is appreciated !!