Theorems · Definition · group theory
MulHom.pi
{I : Type u} →
{f : I → Type v} →
[inst : (i : I) → Mul (f i)] → {γ : Type w} → [inst_1 : Mul γ] → ((i : I) → γ →ₙ* f i) → γ →ₙ* (i : I) → f iA family of MulHom's f a : γ →ₙ* β a defines a MulHom MulHom.pi f : γ →ₙ* Π a, β a
given by MulHom.pi f x b = f b x.
- Defined in
- Mathlib.Algebra.Group.Pi.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MulHomstatement and proof · cited by 299
Cited by9
Results whose statement or proof uses this declaration.
- MonoidHom.piproof · cited by 9
- MulHom.pi_injectivestatement and proof · cited by 4
- NonUnitalRingHom.piproof · cited by 4
- MulHom.pi_applystatement and proof · cited by 1
- MulHom.piMapproof · cited by 1
- Pi.mulHom_injectivestatement · cited by 0
- Pi.mulHomproof · cited by 0
- Pi.mulHom_applystatement · cited by 0
- MulHom.injective_pistatement · cited by 0