Theorems · Definition · group theory
smulMonoidWithZeroHom
{M₀ : Type u_5} →
{N₀ : Type u_6} →
[inst : MonoidWithZero M₀] →
[inst_1 : MulZeroOneClass N₀] →
[inst_2 : MulActionWithZero M₀ N₀] → [IsScalarTower M₀ N₀ N₀] → [SMulCommClass M₀ N₀ N₀] → M₀ × N₀ →*₀ N₀Scalar multiplication as a monoid homomorphism with zero.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsScalarTowerstatement and proof · cited by 3,896
- MonoidHomproof · cited by 3,629
- SMulCommClassstatement and proof · cited by 1,927
- MonoidWithZeroHomstatement · cited by 704
- MonoidWithZerostatement and proof · cited by 456
- MulZeroOneClassstatement and proof · cited by 184
- MonoidHom.toOneHomproof · cited by 132
- OneHom.toFunproof · cited by 132
- MulActionWithZerostatement and proof · cited by 79
- smulMonoidHomproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- smulMonoidWithZeroHom_applystatement and proof · cited by 0