Installing Apple TV in an adjacent closet

There is a recommended HDMI cable length limitation. U will have to find whether you are just a little bit off or way off.

For people who wants to wire HDMI a lot longer than the recommended, I hear there is an HDMI through CAT5/6 product, but I have no idea how expensive they are nor is aware if you will sacrificing video quality.

As for the remote, you are looking for IR extender.

 

You might be able to do it with a IR extender/repeater and a wireless hdmi adapter...

Hard to say much mores due to the utter lack of details you provided.

 

Do you not have any HDMI inputs on your receiver in the closet? That would be the simplest.

 

Then the problem becomes cable length limitation receiver -> TV, we have solved nothing.

 

when reading i assumed the receiver was connected to the tv already, and that the length problem was solved. something is already connected to the tv no? unless this is a new project and i missed that

 

Yes, I assumed the same, hence my initial comment. It's implied that the home theater is already in place. If it's relatively modern, there should be HDMI inputs on the receiver.