Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.whiskerLeft_id
∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] (X Y : C),
CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.CategoryStruct.id Y) =
CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 52 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.
Cites6
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.idstatement · cited by 6,235
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement · cited by 915
Cited by52
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.tensorHom_idproof · cited by 67
- CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fstproof · cited by 6
- CategoryTheory.MonoidalClosed.uncurry_id_eq_evproof · cited by 6
- CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δproof · cited by 4
- CategoryTheory.MonoidalCategory.whiskerLeft_eqToHomproof · cited by 4
- CategoryTheory.MonoidalCategory.whiskerLeft_inv_homproof · cited by 4
- CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unitproof · cited by 4
- CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_homproof · cited by 3
- CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_homproof · cited by 3
- Action.rightUnitor_hom_homproof · cited by 2