Matching inputs and outputs
Having a 4K display or projector might be cool and all but remember that this is only relevant when the content you play also has as at least the 4K resolution! If your input signals have a lower resolution that does not match the same 4K quality, the image will be upscaled and you won’t be able to enjoy your extra pixels. The visual quality is not on par with content natively produced in 4K. This is also why the lack of 8K mainstream content is holding back the boom of 8K visualization systems.
The same logic applies the other way around. Most projectors accept a resolution input that’s higher than their native resolution. However, to cope with the higher resolution, the projectors will compress and adapt the image that is received into fewer pixels. So, you can project 4K content with an HD projector, but it does not make much sense, as you will never see the 4K result projected…
So, in short, to have the best 4K experience, the inputs and outputs of your system should both support this 4K resolution.