Theorems · Definition · category theory
CategoryTheory.MonoidalCategoryStruct.tensorHom
{C : Type u} →
{𝒞 : CategoryTheory.Category.{v, u} C} →
[self : CategoryTheory.MonoidalCategoryStruct C] →
{X₁ Y₁ X₂ Y₂ : C} →
(X₁ ⟶ Y₁) →
(X₂ ⟶ Y₂) →
(CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂ ⟶
CategoryTheory.MonoidalCategoryStruct.tensorObj Y₁ Y₂)Tensor product of identity maps is the identity: 𝟙 X₁ ⊗ₘ 𝟙 X₂ = 𝟙 (X₁ ⊗ X₂)
- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 587 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 9 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategoryStructstatement and proof · cited by 26
Cited by687
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.tensorproof · cited by 91
- CategoryTheory.MonoidalCategory.whiskerLeft_compproof · cited by 82
- CategoryTheory.MonoidalCategory.comp_whiskerRightproof · cited by 76
- CategoryTheory.MonoidalCategory.tensorHom_idstatement · cited by 67
- CategoryTheory.MonoidalCategory.tensorHom_defstatement · cited by 58
- CategoryTheory.MonoidalCategory.id_tensorHomstatement · cited by 57
- CategoryTheory.MonoidalCategory.whiskerRight_tensorproof · cited by 37
- CategoryTheory.MonoidalCategory.tensor_whiskerLeftproof · cited by 37
- CategoryTheory.MonoidalCategory.whisker_exchangeproof · cited by 36
- CategoryTheory.MonoidalCategory.whisker_assocproof · cited by 31
- CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHomstatement · cited by 31
- CategoryTheory.MonoidalCategory.tensorIsoproof · cited by 27
Showing the 200 most cited of 687.