Theorems · Definition · category theory

CategoryTheory.GradedObject.Monoidal.leftUnitor

{I : Type u} →
  [inst : AddMonoid I] →
    {C : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          [inst_3 : DecidableEq I] →
            [inst_4 : CategoryTheory.Limits.HasInitial C] →
              [inst_5 :
                  ∀ (X₂ : C),
                    CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C)
                      ((CategoryTheory.MonoidalCategory.curriedTensor C).flip.obj X₂)] →
                (X : CategoryTheory.GradedObject I C) →
                  CategoryTheory.GradedObject.Monoidal.tensorObj CategoryTheory.GradedObject.Monoidal.tensorUnit X ≅ X

The left unitor isomorphism for graded objects.

Defined in

Mathlib.CategoryTheory.GradedObject.Monoidal

Cited by

4 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryDecidableEqCategoryTheory.Limits.HasInitialCategoryTheory.Limits.PreservesColimit