Explore a detailed academic lecture where Oxford University postdoc Matthew Yu delves into the classification of fusion 2-categories and their role in quantum field theories. Learn how these mathematical structures describe the fusion of 2-spacetime-dimensional surface operators and symmetries in (2+1)d quantum field theories. Discover the classification methodology using braided fusion categories and group cohomological data, with emphasis on the crucial equivalence between the 3-groupoid of (multi)fusion 2-categories and BZ/2-equivariant space commuting squares. Gain insights into the mathematical aspects of quantum field and string theory through the lens of homotopy theory and higher fusion categories, presented as part of the BIMSA-Tsinghua Quantum Symmetry Seminar series.