  We discuss a variety of codimension-one, non-invertible topological defects
in general 3+1d QFTs with a discrete one-form global symmetry. These include
condensation defects from higher gauging of the one-form symmetries on a
codimension-one manifold, each labeled by a discrete torsion class, and duality
and triality defects from gauging in half of spacetime. The universal fusion
rules between these non-invertible topological defects and the one-form
symmetry surface defects are determined. Interestingly, the fusion coefficients
are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases,
$\mathbb{Z}_N$ gauge theories, and $U(1)_N$ Chern-Simons theories. The
associativity of these algebras over TQFT coefficients relies on nontrivial
facts about 2+1d TQFTs. We further prove that some of these non-invertible
symmetries are intrinsically incompatible with a trivially gapped phase,
leading to nontrivial constraints on renormalization group flows. Duality and
triality defects are realized in many familiar gauge theories, including free
Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, ${\cal
N}=1,$ and ${\cal N}=4$ super Yang-Mills theories.
