  Inspired by recent developments generalizing Jordan-Wigner dualities to
higher dimensions, we develop a framework of such dualities using an algebraic
formalism for translation-invariant Hamiltonians proposed by Haah. We prove
that given a translation-invariant fermionic system with general $q$-body
interactions, where $q$ is even, a local mapping preserving global fermion
parity to a dual Pauli spin model exists and is unique up to a choice of basis.
Furthermore, the dual spin model is constructive, and we present various
examples of these dualities. As an application, we bosonize fermionic systems
where free-fermion hopping terms are absent ($q \ge 4$) and fermion parity is
conserved on submanifolds such as higher-form, line, planar or fractal
symmetry. For some cases in 3+1D, bosonizing such a system can give rise to
fracton models where the emergent particles are immobile but yet can behave in
certain ways like fermions. These models may be examples of new nonrelativistic
't Hooft anomalies. Furthermore, fermionic subsystem symmetries are also
present in various Majorana stabilizer codes, such as the color code or the
checkerboard model, and we give examples where their duals are cluster states
or new fracton models distinct from their doubled CSS codes.
