We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom-up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction, we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p ≥ 0 in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (-m)-form symmetries for m ≥ 2. We show that the bulk dual of a topological symmetry operator is not purely topological. This is because the bulk symmetry operator must source stress energy in the sense that these operators are now sensitive to small fluctuations in the metric. As such, they cannot be purely topological. While detailed properties of the resulting object in gravity are model-dependent, we can also extract some qualitative properties of the resulting brane action worldvolume theory. The existence of a symmetry operator in the boundary CFT allows us to predict the existence of a brane in the gravitational bulk. We also revisit the no global symmetries proof given in [36,37], showing how to also cover the case of non-invertible symmetries which fuse to condensation defects. We also comment on the construction of (-m)-form symmetries of a general QFT for m ≥ 2, as well as their holographic dual description in the context of the AdS/CFT correspondence. We conclude by briefly discussing some potential extensions to more general spacetimes.We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom-up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction, we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p ≥ 0 in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (-m)-form symmetries for m ≥ 2. We show that the bulk dual of a topological symmetry operator is not purely topological. This is because the bulk symmetry operator must source stress energy in the sense that these operators are now sensitive to small fluctuations in the metric. As such, they cannot be purely topological. While detailed properties of the resulting object in gravity are model-dependent, we can also extract some qualitative properties of the resulting brane action worldvolume theory. The existence of a symmetry operator in the boundary CFT allows us to predict the existence of a brane in the gravitational bulk. We also revisit the no global symmetries proof given in [36,37], showing how to also cover the case of non-invertible symmetries which fuse to condensation defects. We also comment on the construction of (-m)-form symmetries of a general QFT for m ≥ 2, as well as their holographic dual description in the context of the AdS/CFT correspondence. We conclude by briefly discussing some potential extensions to more general spacetimes.