Yang-Mills theory and Yang-Baxter equations are two very influential concepts in theoretical particle physics and many-body physics. At the first sight, they seemed to be  unrelated to each other. However, recent progress in understanding topological phases and many-body entanglement reveal that there is a deep connection between them. In this talk, I will try to explain, from physicists' point of view, how a universal mathematical structure, called category theory, constitutes a conceptual framework that naturally unites both Yang-Mills and Yang-Baxter.  It is expected that category theory will also provide powerful algebraic techniques for theoretical physics in the future.