  We investigate the behavior of higher-form symmetries at various quantum
phase transitions. We consider discrete 1-form symmetries, which can be either
part of the generalized concept "categorical symmetry" (labelled as
$\tilde{Z}_N^{(1)}$) introduced recently, or an explicit $Z_N^{(1)}$ 1-form
symmetry. We demonstrate that for many quantum phase transitions involving a
$Z_N^{(1)}$ or $\tilde{Z}_N^{(1)}$ symmetry, the following expectation value $
\langle \left( \log O_\mathcal{C} \right)^2 \rangle$ takes the form $\langle
\left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}{\epsilon} P+ b \log
P $, where $O_\mathcal{C}$ is an operator defined associated with loop
$\mathcal{C}$ (or its interior $\mathcal{A}$), which reduces to the Wilson loop
operator for cases with an explicit $Z_N^{(1)}$ 1-form symmetry. $P$ is the
perimeter of $\mathcal{C}$, and the $b \log P$ term arises from the sharp
corners of the loop $\mathcal{C}$, which is consistent with recent numerics on
a particular example. $b$ is a universal microscopic-independent number, which
in (2+1)d is related to the universal conductivity at the quantum phase
transition. $b$ can be computed exactly for certain transitions using the
dualities between (2+1)d conformal field theories developed in recent years. We
also compute the "strange correlator" of $O_\mathcal{C}$: $S_{\mathcal{C}} =
\langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle$ where
$|0\rangle$ and $|1\rangle$ are many-body states with different topological
nature.
