Generalized forms of types N = 1, 2 and higher gauge theory

We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and groups, including the associated higher Maurer–Cartan forms and equations. Using generalized forms of types N = 1, 2, we then provide a complete description of higher gauge structures. Finally, we derive the action functionals for higher Chern–Simons and Yang–Mills theories as applications of the formalism.