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In this article, we give a concise summary of    L  ∞   ‐algebras viewed in terms of Chevalley–Eilenberg algebras, Weil algebras and invariant polynomials and their use in defining connections in higher gauge theory. Using this, we discuss the example of the string Lie 2‐algebra in both the skeletal and the loop model. In both cases, we show how to arrive at the twisted Weil algebras which were used in [1] to construct a non‐abelian self‐dual string soliton, see also [2–4].

Twisted Weil Algebras for the String Lie 2‐Algebra