Are TV coaxial cables compatible with WiFi antennas?
So you want to transport that 2.5 GHz (or even 5 GHz ?) Wifi signal over TV COAX cable ?

Indeed to the non-RF people you'd just think that would work. And it does BUT there will be almost no signal coming through that cable.

The Wifi signal will be attenuated so much in that COAX cable that it will defeat the whole purpose of having an antenna on the roof. The same antenna directly on the router might even get better coverage.

Why is that ?

TV COAX cables are not designed for 2.5 GHz signals, TV signals go up to 1 GHz and even at that frequency you can expect a lot of attenuation.

TV COAX cables usually have a characteristic impedance of 75 ohms, Wifi antennas routers etc. all use 50 ohms. There are no exceptions to that.

So no, in practice this will not work at all.