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Theorems · Definition · group theory

Pi.evalAddHom

{I : Type u} → (f : I → Type v) → [inst : (i : I) → Add (f i)] → (i : I) → ((i : I) → f i) →ₙ+ f i

Evaluation of functions into an indexed collection of additive semigroups at a point is an additive semigroup homomorphism. This is Function.eval i as an AddHom.

Defined in
Mathlib.Algebra.Group.Pi.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Pi.evalNonUnitalStarAlgHom · cited by 3Pi.evalNonUnitalStarAlgHomAddHom.piMap · cited by 1AddHom.piMapMatrix.entryAddHom_eq_comp · cited by 0Matrix.entryAddHom_eq_compPi.evalAddHom_apply · cited by 0Pi.evalAddHom_applyAddHom · cited by 294AddHomPi.add_apply · cited by 61Pi.add_applyPi.evalAddHomCITED BYCITES

Cites2

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Cited by4

Results whose statement or proof uses this declaration.