Theorems · Definition · group theory
Pi.evalMulHom
{I : Type u} → (f : I → Type v) → [inst : (i : I) → Mul (f i)] → (i : I) → ((i : I) → f i) →ₙ* f iEvaluation of functions into an indexed collection of semigroups at a point is a semigroup
homomorphism.
This is Function.eval i as a MulHom.
- Defined in
- Mathlib.Algebra.Group.Pi.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Mul
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.
- MulHomstatement · cited by 299
- Pi.mul_applyproof · cited by 24
Cited by5
Results whose statement or proof uses this declaration.
- Pi.evalNonUnitalStarAlgHomproof · cited by 3
- Pi.evalNonUnitalRingHomproof · cited by 1
- MulHom.piMapproof · cited by 1
- Pi.evalMulHom_applystatement and proof · cited by 0
- Pi.evalNonUnitalStarAlgHom_applystatement · cited by 0