We explore topological defects in the 4-dimensional pure $\mathbb {Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb {Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley [1] for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form $\mathbb {Z}_{2}$ symmetry defects as well as the junctions among KWW duality defects and 1-form $\mathbb {Z}_{2}$ center symmetry defects. The crossing relations among these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.

We explore topological defects in the 4-dimensional pure Z 2 lattice gauge theory. This theory has 1-form Z 2 center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley [1] for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form Z 2 symmetry defects as well as the junctions among KWW duality defects and 1-form Z 2 center symmetry defects. The crossing relations among these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.