Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.tensorHom_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X₁ X₂ : C}
(f : X₁ ⟶ X₂) (Y : C),
CategoryTheory.MonoidalCategoryStruct.tensorHom f (CategoryTheory.CategoryStruct.id Y) =
CategoryTheory.MonoidalCategoryStruct.whiskerRight f Y- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 67 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.comp_idproof · cited by 2,119
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
- CategoryTheory.MonoidalCategory.tensorHom_defproof · cited by 58
- CategoryTheory.MonoidalCategory.whiskerLeft_idproof · cited by 52
Cited by67
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.tensor_whiskerLeftproof · cited by 37
- CategoryTheory.MonoidalCategory.whiskerRight_tensorproof · cited by 37
- CategoryTheory.MonoidalCategory.whisker_assocproof · cited by 31
- CategoryTheory.MonoidalCategory.comp_tensor_idproof · cited by 5
- CategoryTheory.MonoidalCategory.tensorμ_natural_leftproof · cited by 5
- CategoryTheory.MonoidalCategory.tensorμ_natural_rightproof · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unitproof · cited by 4
- CategoryTheory.Adjunction.unit_app_tensor_comp_map_δproof · cited by 3
- CategoryTheory.MonoidalCategory.tensor_hom_inv_idproof · cited by 1
- CategoryTheory.MonoidalCategory.tensor_hom_inv_id'proof · cited by 1