The biosphere is part of the carbon cycle, but what if there were no biosphere? Is the biosphere necessary for the carbon cycle?

Yes, the biosphere is necessary for the carbon cycle. The biosphere is the part of the Earth's system where living organisms exist and interact with each other and their environment. It is the source of carbon for the carbon cycle, as organisms take in carbon dioxide from the atmosphere and release it back into the atmosphere through respiration and decomposition. Without the biosphere, there would be no source of carbon for the carbon cycle, and the cycle would be disrupted.