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Theorems · Definition · ring theory

DirectSum.gMulHom

{ι : Type u_1} →
  (A : ι → Type u_2) →
    [inst : Add ι] →
      [inst_1 : (i : ι) → AddCommMonoid (A i)] →
        [DirectSum.GNonUnitalNonAssocSemiring A] → {i j : ι} → A i →+ A j →+ A (i + j)

The piecewise multiplication from the Mul instance, as a bundled homomorphism.

Defined in
Mathlib.Algebra.DirectSum.Ring
Cited by
3 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
AddAddCommMonoidDirectSum.GNonUnitalNonAssocSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DirectSum.mul_eq_dfinsuppSum · cited by 3DirectSum.mul_eq_dfinsupp…DirectSum.mulHom · cited by 2DirectSum.mulHomDirectSum.gMulHom_apply_apply · cited by 2DirectSum.gMulHom_apply_a…DirectSum.mulHom_of_of · cited by 1DirectSum.mulHom_of_ofAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomGradedMonoid.GMul.mul · cited by 45GMul.mulDirectSum.GNonUnitalNonAssocSemiring · cited by 10DirectSum.GNonUnitalNonAs…DirectSum.GNonUnitalNonAssocSemiring.mul_add · cited by 0GNonUnitalNonAssocSemirin…DirectSum.GNonUnitalNonAssocSemiring.mul_zero · cited by 0GNonUnitalNonAssocSemirin…DirectSum.gMulHomCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.