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In rough paths theory, the signature of a path $x: [0, T] \to \mathbb{R}^d$ is an element in the tensor algebra $T((\mathbb{R}^d))$. These signatures reside within the group-like elements and ...

In Hairer's notes A Theory of Regularity Structures he defines automorphisms of a regularity structure on page 28. I will recall the definition here: Is there any way of extending this to morphisms ...