Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.id_tensorHom
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X : C)
{Y₁ Y₂ : C} (f : Y₁ ⟶ Y₂),
CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id X) f =
CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement and proof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
- CategoryTheory.MonoidalCategory.tensorHom_defproof · cited by 58
- CategoryTheory.MonoidalCategory.id_whiskerRightproof · cited by 48
Cited by57
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.tensor_whiskerLeftproof · cited by 37
- CategoryTheory.MonoidalCategory.whisker_assocproof · cited by 31
- CategoryTheory.MonoidalCategory.tensorμ_natural_rightproof · cited by 5
- CategoryTheory.MonoidalCategory.id_tensor_compproof · cited by 4
- CategoryTheory.GradedObject.Monoidal.ιTensorObj₃_tensorHomproof · cited by 2
- CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_leftproof · cited by 1
- CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_rightproof · cited by 1
- Action.diagonalSuccIsoTensorTrivial_inv_hom_applyproof · cited by 1
- HomologicalComplex.rightUnitor'_invproof · cited by 1
- CategoryTheory.GradedObject.Monoidal.pentagon_invproof · cited by 1
- CategoryTheory.μ_naturalityᵣproof · cited by 1
- CategoryTheory.MonoidalCategory.pentagon_hom_invproof · cited by 1