Theorems · Theorem · category theory

CategoryTheory.ModObj.one_smul_self

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] (M : C)
  [inst_2 : CategoryTheory.MonObj M] (X : C) [inst_3 : CategoryTheory.ModObj M X],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.MonObj.one X)
      CategoryTheory.ModObj.smul =
    (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom

Defined in: Mathlib.CategoryTheory.Monoidal.Mod
Cited by: 1 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.MonObj CategoryTheory.ModObj

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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 · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
CategoryTheory.MonObjstatement and proof · cited by 199
CategoryTheory.MonObj.onestatement · cited by 189
CategoryTheory.ModObjstatement and proof · cited by 38

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ModObj.one_smul_self_assocproof · cited by 0