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Theorems · Definition · group theory

MonoidHom.piMap

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

A family of monoid homomorphisms f i : M i →* N i defines a monoid homomorphism MonoidHom.piMap f : (Π i, M i) →* (Π i, N i) given by MonoidHom.piMap f x i = f i x. This is Pi.map for MonoidHoms.

Defined in
Mathlib.Algebra.Group.Pi.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MonoidHom.piMap_apply · cited by 0MonoidHom.piMap_applyMonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassMonoidHom.comp · cited by 469MonoidHom.compPi.evalMonoidHom · cited by 14Pi.evalMonoidHomMonoidHom.pi · cited by 9MonoidHom.piMonoidHom.piMapCITED BYCITES

Cites5

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.