  Non-invertible symmetries have by now seen numerous constructions in higher
dimensional Quantum Field Theories (QFT). In this paper we provide an in depth
study of gauging 0-form symmetries in the presence of non-invertible
symmetries. The starting point of our analysis is a theory with $G$ 0-form
symmetry, and we propose a description of sequential partial gaugings of
sub-symmetries. The gauging implements the theta-symmetry defects of the
companion paper [1]. The resulting network of symmetry structures related by
this gauging will be called a non-invertible symmetry web. Our formulation
makes direct contact with fusion 2-categories, and we uncover numerous
interesting structures such as symmetry fractionalization in this categorical
setting. The complete symmetry web is derived for several groups $G$, and we
propose extensions to higher dimensions. The highlight of this analysis is the
complete categorical symmetry web, including non-invertible symmetries, for 3d
pure gauge theories with orthogonal gauge groups and its extension to arbitrary
dimensions.
