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Theorems · Definition · group theory

MulHom.single

{ι : Type u_1} →
  {α : ι → Type u_2} → [inst : (i : ι) → MulZeroClass (α i)] → [DecidableEq ι] → (i : ι) → α i →ₙ* (i : ι) → α i

The multiplicative homomorphism including a single MulZeroClass into a dependent family of MulZeroClasses, as functions supported at a point. This is the MulHom version of Pi.single.

Defined in
Mathlib.Algebra.GroupWithZero.Pi
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
MulZeroClassDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Pi.single_mul · cited by 3Pi.single_mulMulHom.single_apply · cited by 0MulHom.single_applyPi.single · cited by 518Pi.singleMulHom · cited by 299MulHomMulZeroClass · cited by 232MulZeroClassMulHom.singleCITED BYCITES

Cites3

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

Cited by2

Results whose statement or proof uses this declaration.