Recent advances in digital twins (DTs) provide an unprecedented opportunity to develop sustainability-aware cognitive intelligence in manufacturing systems. However, most DT work focuses more on real-time data streaming, visualization and predictive analytics, but places less focus on multi-agent intelligence. For example, DT-supported production scheduling is often constrained by centralized, single-objective optimization, which cannot handle multi-agent learning and multiple objectives simultaneously. Therefore, this paper proposes a new cognitive digital twin (CDT) for multi-objective production scheduling through decentralized, collaborative multi-agent learning towards the sustainable manufacturing practice. CDT embodies the decentralized learning of heterogeneous agents, including machines, automated guided vehicles (AGVs), automated storage and retrieval systems (ASRS), to balance individual and collective objectives. First, we develop a multi-objective optimization algorithm that aligns production schedules with time-varying market demands, and diverse objectives such as throughput, task transition efficiency, workload balance, as well as energy efficiency. Second, a decentralized learning approach enables intelligent agents to make autonomous, collaborative scheduling decisions, facilitating collective optimization in real-time. Each agent within the manufacturing system operates independently with the capability of cognitive learning, making real-time adjustments aligned with overarching objectives. By fostering this decentralized cognitive intelligence, this new CDT enhances resilience and adaptability in complex, interconnected environments, ultimately improving the productivity and sustainability. Third, we evaluate and validate the CDT model through computer experiments, demonstrating superior improvements in task allocation, resource utilization, and sustainability. This research shows strong promise to develop advanced CDT technology for next-generation smart and sustainable manufacturing.