After Taizu died, his grandson Zhu Yunwen succeeded to the throne.
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太祖 and 高祖 mark a founder, 太宗 the second ruler: 明太祖朱元璋, 清太祖努尔哈赤. A dynasty could also give the title to an ancestor who never reigned: when 曹丕 founded the Wei, his father 曹操 became 魏太祖.