I don't understand the meaning of carrier frequency with respect to a transmission channel and the modulation phase with respect to the carrier frequency. I'm at a beginning level, so I try to explain what I get: "the carrier frequency of a channel is that frequency at which a channel works in the sense that the signals with that frequency are well transmitted by the channel". For example, Wi-Fi works either 2.4 GHz or 5 GHz carrier frequency.
The bandwidth of a channel is the set of frequencies a channel can transmit. But what is the meaning of bandwidth of a channel with respect its carrier frequency? If Wi-Fi works with a bandwidth of 10 MHz and it has a carrier frequency of 2.4 GHz means that all signals with frequency x where 2.4 Ghz - 5 MHz <= x <= 2.4Ghz + 5 MHz are well transmitted?
Instead, the modulation process is that process in charge of shifting/moving the input signal into the carrier frequency of the channel. Why do I need to use modulation? Because usually channels work with higher frequencies than frequencies of input signals and this is a suitable way to transmit information through a channel.