Theorems · Theorem · category theory
CategoryTheory.Linear.smulOfRingMorphism_smul_eq
∀ {R : Type w} [inst : Ring R] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
[inst_2 : CategoryTheory.Preadditive C] (φ : R →+* CategoryTheory.CatCenter C) {X Y : C} (a : R) (f : X ⟶ Y),
a • f = CategoryTheory.CategoryStruct.comp ((φ a).app X) f- Defined in
- Mathlib.CategoryTheory.Center.Linear
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.CatCenterstatement and proof · cited by 53
- CategoryTheory.CatCenter.appstatement · cited by 31
- CategoryTheory.Linear.smulOfRingMorphismstatement · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Linear.smulOfRingMorphism_smul_eq'proof · cited by 0