  We study non-invertible duality symmetries by gauging a diagonal subgroup of
a non-anomalous U(1) $\times$ U(1) global symmetry. In particular, we employ
the half-space gauging to $c=2$ bosonic torus conformal field theory (CFT) in
two dimensions and pure U(1) $\times$ U(1) gauge theory in four dimensions. In
$c=2$ bosonic torus CFT, we show that the non-invertible symmetry obtained from
the diagonal gauging becomes emergent on an irrational CFT point. We also
calculate the fusion rules concerning the duality defect. We find out that the
fusion algebra is non-commutative. We also obtain a similar result in pure U(1)
$\times$ U(1) gauge theory in four dimensions.
