Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] (X : C)
{Y Z : C} (f : Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f)
(CategoryTheory.SemiCartesianMonoidalCategory.snd X Z) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y) f- Cited by
- 19 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement and proof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.leftUnitorproof · cited by 437
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.tensorHom_sndproof · cited by 12
- CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd_assocproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeftproof · cited by 6
- CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fstproof · cited by 5
- CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_sndproof · cited by 5
- CategoryTheory.GrpObj.whiskerLeft_η_commutatorproof · cited by 2
- CategoryTheory.AddGrpObj.whiskerLeft_η_addCommutatorproof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_sndproof · cited by 1
- CategoryTheory.mul_add_iffproof · cited by 1
- SSet.stdSimplex.ι₀_whiskerLeft_toSSetObjI_μproof · cited by 1