Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.whiskerRight_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y : C}
(f : X ⟶ Y),
CategoryTheory.MonoidalCategoryStruct.whiskerRight f (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom
(CategoryTheory.CategoryStruct.comp f (CategoryTheory.MonoidalCategoryStruct.rightUnitor Y).inv)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 38 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.
Cites14
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.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- 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.Category.comp_idproof · cited by 2,119
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.rightUnitorstatement and proof · cited by 397
Cited by38
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.whiskerRight_fstproof · cited by 13
- CategoryTheory.MonoidalCategory.rightUnitor_inv_naturalityproof · cited by 4
- CategoryTheory.MonoidalCategory.whiskerRight_id_assocproof · cited by 4
- CategoryTheory.MonObj.extproof · cited by 3
- CategoryTheory.MonoidalCategory.tensor_left_unitalityproof · cited by 3
- CategoryTheory.MonoidalCategory.tensor_right_unitalityproof · cited by 3
- Bimod.TensorBimod.actRight_one'proof · cited by 3
- CategoryTheory.AddMonObj.extproof · cited by 3
- CategoryTheory.HopfObj.one_antipodeproof · cited by 2
- CategoryTheory.Enriched.FunctorCategory.enriched_comp_idproof · cited by 2
- CategoryTheory.Iso.eHomCongr_compproof · cited by 2