Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (X Y : C),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.SemiCartesianMonoidalCategory.toUnit X) Y)
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor Y).hom =
    CategoryTheory.SemiCartesianMonoidalCategory.snd X Y

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory

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Cites21

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 and proof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · 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.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement and proof · cited by 437

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom_assocproof · cited by 0