Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionHom

∀ (C : Type u_1) (D : Type u_2) [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.MonoidalCategory C] [inst_2 : CategoryTheory.Category.{v_2, u_2} D]
  [inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction Cᵒᵖ Dᵒᵖ] {c c' : C} {d d_1 : D} (f : c ⟶ c')
  (g : d ⟶ d_1),
  CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom f g =
    (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom f.op g.op).unop

Defined in: Mathlib.CategoryTheory.Monoidal.Action.Opposites
Cited by: 0 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.Category CategoryTheory.MonoidalCategory.MonoidalLeftAction

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites11

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
Oppositestatement and proof · cited by 8,081
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
Opposite.unopstatement · cited by 2,231
Quiver.Hom.opstatement · cited by 1,948
Quiver.Hom.unopstatement · cited by 903
CategoryTheory.MonoidalCategory.MonoidalLeftActionstatement and proof · cited by 215
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObjstatement · cited by 185
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomstatement and proof · cited by 31
CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftActionstatement · cited by 11

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.