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Theorems · Definition · group theory

MulHom.piMap

{ι : Type u_1} →
  {M : ι → Type u_3} →
    {N : ι → Type u_4} →
      [inst : (i : ι) → Mul (M i)] →
        [inst_1 : (i : ι) → Mul (N i)] → ((i : ι) → M i →ₙ* N i) → ((i : ι) → M i) →ₙ* (i : ι) → N i

A family of MulHom's f i : M i →ₙ* N i defines a MulHom MulHom.piMap f : (Π i, M i) →ₙ* (Π i, N i) given by MulHom.piMap f x i = f i x. This is Pi.map for MulHoms.

Defined in
Mathlib.Algebra.Group.Pi.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
MulMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulHom.piMap_apply · cited by 0MulHom.piMap_applyMulHom · cited by 299MulHomMulHom.comp · cited by 44MulHom.compMulHom.pi · cited by 5MulHom.piPi.evalMulHom · cited by 2Pi.evalMulHomMulHom.piMapCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.