Theorems · Definition · ring theory
GradedMonoid.GSMul.smul
{ιA : Type u_1} →
{ιM : Type u_3} →
{A : ιA → Type u_4} →
{M : ιM → Type u_5} →
{inst : VAdd ιA ιM} → [self : GradedMonoid.GSMul A M] → {i : ιA} → {j : ιM} → A i → M j → M (i +ᵥ j)The homogeneous multiplication map smul
- Defined in
- Mathlib.Algebra.GradedMulAction
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- GradedMonoid.GSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- HVAdd.hVAddstatement · cited by 1,820
- VAddstatement and proof · cited by 616
- GradedMonoid.GSMulstatement and proof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- DirectSum.gsmulHomproof · cited by 2
- DirectSum.Gmodule.smulAddMonoidHom_apply_of_ofstatement and proof · cited by 1
- DirectSum.gsmulHom_apply_applystatement · cited by 1
- DirectSum.GdistribMulAction.casesOnstatement and proof · cited by 0
- DirectSum.GdistribMulAction.noConfusionproof · cited by 0
- DirectSum.GdistribMulAction.noConfusionTypeproof · cited by 0
- DirectSum.GdistribMulAction.recOnstatement and proof · cited by 0
- DirectSum.GdistribMulAction.smul_addstatement · cited by 0
- DirectSum.GdistribMulAction.smul_zerostatement · cited by 0
- DirectSum.Gmodule.add_smulstatement · cited by 0
- DirectSum.Gmodule.casesOnstatement and proof · cited by 0
- GradedMonoid.mk_smul_mkstatement · cited by 0