if you have a set X acting as a domain and also have some set T acting as a representation by being paired with an interpretation [⋅] : T ≅ T' ⊆ (X → X) which places T within the space of transformations over X, and if you happen to have a value x₀ ∈ X for which the mapping grnd : t ↦ [t](x₀) is surjective onto X, then you can identify values x ∈ X with transformations grnd⁻¹(x) and then since grnd(f ∘ grnd⁻¹(x)) = f(x) you get to use ∘ as both transformation composition and transformation application