The paper by Iñaki García Etxebarria and Saghar S. Hosseini explores the symmetry structure of quantum field theories (QFTs) and their associated symmetry theories (SymTFTs). The authors focus on geometrically engineered QFTs in string theory, where the SymTFT arises from the background geometry through the integration of the topological sector of string theory on the horizon of the geometry transverse to the QFT locus. They clarify subtle aspects of this proposal by taking a higher-dimensional approach, where the ten-dimensional string theory fields are integrated as edge modes of an eleven-dimensional topological field theory. The main goal is to understand the emergence of the $BF$ sector in the SymTFT, which is derived from integrating an auxiliary theory in one dimension higher. The authors use the Hopkins-Singer formalism to study differential cohomology and demonstrate how the $BF$ theory can be obtained by reducing the Chern-Simons action on the internal manifold $L$ and understanding the effective theory on a manifold with boundary. The paper includes detailed examples, such as the $U(1)$ theory in two dimensions, $U(1) \times U(1)$ theory in even dimensions, and the $BF$ theory on a space with boundary, to illustrate the concepts and techniques used. They also discuss the application of these methods to supersymmetric QFTs obtained by placing string theory or M-theory at isolated conical singularities, focusing on the $d=5$ SCFTs arising from M-theory on singular Calabi-Yau threefolds. The authors aim to provide a clearer understanding of the SymTFT and its role in understanding the symmetry structures of QFTs, particularly in the context of string theory and M-theory. They expect that their approach, which involves a modification of the Hopkins-Singer formalism, will also help in recovering the anomaly theory in cases where the mathematical formalism is well understood.The paper by Iñaki García Etxebarria and Saghar S. Hosseini explores the symmetry structure of quantum field theories (QFTs) and their associated symmetry theories (SymTFTs). The authors focus on geometrically engineered QFTs in string theory, where the SymTFT arises from the background geometry through the integration of the topological sector of string theory on the horizon of the geometry transverse to the QFT locus. They clarify subtle aspects of this proposal by taking a higher-dimensional approach, where the ten-dimensional string theory fields are integrated as edge modes of an eleven-dimensional topological field theory. The main goal is to understand the emergence of the $BF$ sector in the SymTFT, which is derived from integrating an auxiliary theory in one dimension higher. The authors use the Hopkins-Singer formalism to study differential cohomology and demonstrate how the $BF$ theory can be obtained by reducing the Chern-Simons action on the internal manifold $L$ and understanding the effective theory on a manifold with boundary. The paper includes detailed examples, such as the $U(1)$ theory in two dimensions, $U(1) \times U(1)$ theory in even dimensions, and the $BF$ theory on a space with boundary, to illustrate the concepts and techniques used. They also discuss the application of these methods to supersymmetric QFTs obtained by placing string theory or M-theory at isolated conical singularities, focusing on the $d=5$ SCFTs arising from M-theory on singular Calabi-Yau threefolds. The authors aim to provide a clearer understanding of the SymTFT and its role in understanding the symmetry structures of QFTs, particularly in the context of string theory and M-theory. They expect that their approach, which involves a modification of the Hopkins-Singer formalism, will also help in recovering the anomaly theory in cases where the mathematical formalism is well understood.