Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.tensorHom_def_assoc
∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] {X₁ Y₁ X₂ Y₂ : C}
(f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) {Z : C} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj Y₁ Y₂ ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f g) h =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X₂)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Y₁ g) h)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement and proof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement and proof · cited by 587
- CategoryTheory.MonoidalCategory.tensorHom_defproof · cited by 58
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.HopfObj.one_antipodeproof · cited by 2
- CategoryTheory.Iso.eHomCongr_compproof · cited by 2
- CategoryTheory.Enriched.FunctorCategory.enriched_assocproof · cited by 2
- CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μproof · cited by 1
- CategoryTheory.MonObj.mul_one_homproof · cited by 1
- CategoryTheory.AddMonObj.add_zero_homproof · cited by 1
- CategoryTheory.HopfObj.antipode_antipodeproof · cited by 0
- CategoryTheory.MonoidalClosed.curry'_compproof · cited by 0