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We consider extended Cartan homotopy formula (ECHF) for higher gauge theory.Firstly, we construct an oriented simplex based on 2-connections and presentdifferential and integral forms of the higher ECHF. Then, we study the higherChern-Simons-Antoniadis-Savvidy (ChSAS) theory and prove that the higher ECHFcan reproduce the higher Chern-Weil theorem and give higher triangle equation.We finally conclude from the higher ECHF that a higher transgression form canbe written as the difference of two higher ChSAS forms minus an exact form.

Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory