Is “As the most senior officer, he served as co-commander with Zhou Yu.” true?

The Records of the Three Kingdoms, Book of Wu, Biography of Cheng Pu records that Cheng Pu served Sun Jian, Sun Ce, and Sun Quan in succession, and in the Battle of Red Cliffs, together with Zhou Yu as left and right commanders, he greatly defeated Cao Cao's army: "坚薨，复随孙策在淮南"; "策薨，与张昭等共辅孙权"; "与周瑜为左右督，破曹公于乌林" (Records of the Three Kingdoms, Book of Wu, Biographies of Cheng, Huang, Han, Jiang, Zhou, Chen, Dong, Gan, Ling, Xu, Pan, and Ding).