Theorems · Definition · category theory

CategoryTheory.GradedObject.Monoidal.tensorHom

{I : Type u} →
  [inst : AddMonoid I] →
    {C : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          {X₁ X₂ Y₁ Y₂ : CategoryTheory.GradedObject I C} →
            (X₁ ⟶ X₂) →
              (Y₁ ⟶ Y₂) →
                [inst_3 : X₁.HasTensor Y₁] →
                  [inst_4 : X₂.HasTensor Y₂] →
                    CategoryTheory.GradedObject.Monoidal.tensorObj X₁ Y₁ ⟶
                      CategoryTheory.GradedObject.Monoidal.tensorObj X₂ Y₂

The morphism tensorObj X₁ Y₁ ⟶ tensorObj X₂ Y₂ induced by morphisms of graded objects f : X₁ ⟶ X₂ and g : Y₁ ⟶ Y₂.

Defined in

Mathlib.CategoryTheory.GradedObject.Monoidal

Cited by

23 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensor