The Decarbon Air Rights came into effect in New York City as a solution to climate and housing crisis, allowing buildings with new zoning code, DC(residential buildings under five stories) to trade decarbonizing materials for air rights. Mycelium became a game changer due to its ability to grow its joints to the existing building, lightweightness, and multifunction as exterior material and insulations. By creating a new policy and investigating the building, carbon, material cycle, and related decision-makers, we are looking for a possibility to minimize the carbon emissions by locating the entire material cycle in the city. This material cycle exists within the scale of a building, a block, several blocks, and a city, but does not exist as an enclosed one. Hence, buildings or blocks need to cooperate and exchange with each other, forming an interconnected network. Since mycelium is stronger in compression and weaker in tension, we used compression-only structures with pre-tension form-finding methods and interpreted it in monolith vault, arch, and truss systems. The stereotomic and the tectonic structures are juxtaposed and support different functions; the former compose residential units, and the latter compose bridges and community spaces, emphasizing interdependence and interconnectivity.