Synthetic G-jet-structures in modal homotopy type theory

Journal article, 2024

This article constructs the moduli stack of torsion-free G-jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any infinity-topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are given by the deRham-Stack construction. Homotopy type theory allows a formulation of this abstract theory with surprisingly low complexity. This is witnessed by the accompanying formalization of large parts of this work.