Definition tensorfunctor_comp {C : category} (T : tensor_data C) : UU := ∏ (x y x' y' x'' y'' : C), ∏ (f : C ⟦x,x'⟧) (f' : C ⟦x',x''⟧) (g : C ⟦y,y'⟧) (g' : C ⟦y',y''⟧), (f' ⊗^{T} g') ∘ (f ⊗^{T} g) = (f'∘f) ⊗^{T} (g'∘g).
Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos.