  We study fermionic non-invertible symmetries in (1+1)d, which are generalized
global symmetries that mix fermion parity symmetry with other invertible and
non-invertible internal symmetries. Such symmetries are described by fermionic
fusion supercategories, which are fusion $\pi$-supercategories with a choice of
fermion parity. The aim of this paper is to flesh out the categorical Landau
paradigm for fermionic symmetries. We use the formalism of Symmetry Topological
Field Theory (SymTFT) to study possible gapped and gapless phases for such
symmetries, along with possible deformations between these phases, which are
organized into a Hasse phase diagram. The phases can be characterized in terms
of sets of condensed, confined and deconfined generalized symmetry charges,
reminiscent of notions familiar from superconductivity. Many of the gapless
phases also serve as phase transitions between gapped phases. The associated
fermionic conformal field theories (CFTs) can be obtained by performing
generalized fermionic Kennedy-Tasaki (KT) transformations on bosonic CFTs
describing simpler transitions. The fermionic non-invertible symmetries along
with their charges and phases discussed here can be obtained from those of
bosonic non-invertible symmetries via fermionization or Jordan-Wigner
transformation, which is discussed in detail.
