Theorems · Definition · category theory
CategoryTheory.Linear.smulOfRingMorphism
{R : Type w} →
[inst : Ring R] →
{C : Type u} →
[inst_1 : CategoryTheory.Category.{v, u} C] →
[inst_2 : CategoryTheory.Preadditive C] → (R →+* CategoryTheory.CatCenter C) → (X Y : C) → SMul R (X ⟶ Y)The scalar multiplication by R on the type X ⟶ Y of morphisms in
a category C equipped with a ring morphism R →+* CatCenter C.
- Defined in
- Mathlib.CategoryTheory.Center.Linear
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · 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.appproof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Linear.smulOfRingMorphism_smul_eqstatement · cited by 1
- CategoryTheory.Linear.smulOfRingMorphism_smul_eq'statement · cited by 0