Carbon is fixed in the soil if the compost is damp and aerated. If the compost is too wet and not turned (not aerated), the organic matter rots, giving off methane. Carbon is the gaseous nutrient. It's transformation, into a greenhouse gas, is CO2. But carbon is organic matter in the soil, if treated well there is less gaseous transformation, less reduction of humus and therefore less carbon dioxide in the atmosphere.
All things fall and are built again in a closed-cycle ecology – NO WASTE – and those that build them again are microbial and joyous. Our economics and our ecology can now come home – Oikos – together. To give up on gaseous transformation – aspiration/celebrity – is to act as a collective offensive, or in mutual self defence.