Theorems · Theorem · category theory
CategoryTheory.ModObj.mul_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.mul X)
CategoryTheory.ModObj.smul =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator M M X).hom
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerLeft M CategoryTheory.ModObj.smul) CategoryTheory.ModObj.smul)- Defined in
- Mathlib.CategoryTheory.Monoidal.Mod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
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 · 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.whiskerLeftstatement · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
- CategoryTheory.MonoidalCategoryStruct.associatorstatement · cited by 667
- CategoryTheory.MonObj.mulstatement · cited by 230
- CategoryTheory.MonObjstatement and proof · cited by 199
- CategoryTheory.ModObjstatement and proof · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ModObj.mul_smul_self_flipproof · cited by 1
- CategoryTheory.ModObj.mul_smul_self_assocproof · cited by 0