Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.tensorHom_def
∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] {X₁ Y₁ X₂ Y₂ : C}
(f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂),
CategoryTheory.MonoidalCategoryStruct.tensorHom f g =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X₂)
(CategoryTheory.MonoidalCategoryStruct.whiskerLeft Y₁ g)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
Cited by58
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.tensorHom_idproof · cited by 67
- CategoryTheory.MonoidalCategory.id_tensorHomproof · cited by 57
- CategoryTheory.MonoidalCategory.tensorHom_def'proof · cited by 26
- CategoryTheory.CartesianMonoidalCategory.tensorHom_fstproof · cited by 12
- CategoryTheory.CartesianMonoidalCategory.tensorHom_sndproof · cited by 12
- CategoryTheory.GradedObject.Monoidal.ι_tensorHomproof · cited by 11
- CategoryTheory.BraidedCategory.braiding_naturalityproof · cited by 8
- CategoryTheory.MonoidalCategory.tensorHom_def_assocproof · cited by 8
- CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_appproof · cited by 6
- CategoryTheory.MonoidalCategory.associator_inv_naturalityproof · cited by 4
- CategoryTheory.MonObj.extproof · cited by 3
- CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_homproof · cited by 3