  In this paper, we present a generalization of well-established results
regarding symmetries of $\Bbbk$-algebras, where $\Bbbk$ is a field.
Traditionally, for a $\Bbbk$-algebra $A$, the group $\Bbbk$-algebra
automorphisms of $A$ captures the symmetries of $A$ via group actions.
Similarly, the Lie algebra of derivations of $A$ captures the symmetries of $A$
via Lie algebra actions. In this paper, given a category $\mathcal{C}$ whose
objects possess $\Bbbk$-linear monoidal categories of modules, we introduce an
object $\operatorname{Sym}_{\mathcal{C}}(A)$ that captures the symmetries of
$A$ via actions of objects in $\mathcal{C}$. Our study encompasses various
categories whose objects include groupoids, Lie algebroids, and more generally,
cocommutative weak Hopf algebras. Notably, we demonstrate that for a positively
graded non-connected $\Bbbk$-algebra $A$, some of its symmetries are naturally
captured within the weak Hopf framework.
