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This article constructs the moduli stack of torsionfree $G$-structures inhomotopy type theory with one monadic modality. This yields a construction ofthis moduli stack for any $\infty$-topos equipped with any stable factorizationsystems.  In the intended applications of this theory, the factorization systems aregiven by the deRham-Stack construction. Homotopy type theory allows aformulation of this abstract theory with surprising low complexity. This iswitnessed by the accompanying formalization of large parts of this work.

Cartan Geometry in Modal Homotopy Type Theory