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Battery swapping stations (BSSs) and charging stations (CSs), which provide electric vehicle battery refueling services, are important participants in the electricity and carbon markets. Battery swapping stations (BSSs) and charging stations (CSs), which provide electric vehicle battery refueling services, are important participants in the electricity and carbon markets. The coordination between BSSs and CSs offers a great opportunity for enhancing system flexibility and lowering operation costs, which is underexplored in the literature. Thus, this paper proposes a cooperative operation approach for a BSS, a CS, and a group of residential buildings (RBs) in a community microgrid to minimize their operation costs. These three entities can trade electricity and carbon allowance in the central and local markets. The local electricity and carbon trading problem is formulated using Nash bargaining theory to determine the amounts of electricity and carbon allowance to be traded and the corresponding payments. The Nash bargaining problem is decomposed into an electricity and carbon allowance scheduling problem (P–S1) and a payment bargaining problem (P–S2). The P–S1 is transformed into a mixed-integer linear programming (MILP) problem using a linearization technique, while the closed-form solution to the P–S2 is derived. Compared to the noncooperative benchmark, the proposed approach reduces operation costs of the BSS, CS, and RBs by 49.85%, 67.17%, and 77.24%, and their carbon emissions by 10.52%, 26.73%, and 27.82%. • Cooperation between a battery swapping station and a charging station is proposed. • Nash bargaining theory is used to formulate local electricity and carbon trading. • A linearization technique is employed to solve the Nash bargaining problem. • Impacts of different coalition combinations and market settings are investigated. [ABSTRACT FROM AUTHOR]