Theorems · Theorem · ring theory
DirectSum.gMulHom_apply_apply
∀ {ι : Type u_1} (A : ι → Type u_2) [inst : Add ι] [inst_1 : (i : ι) → AddCommMonoid (A i)]
[inst_2 : DirectSum.GNonUnitalNonAssocSemiring A] {i j : ι} (a : A i) (b : A j),
((DirectSum.gMulHom A) a) b = GradedMonoid.GMul.mul a b- Defined in
- Mathlib.Algebra.DirectSum.Ring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- GradedMonoid.GMul.mulstatement · cited by 45
- DirectSum.GNonUnitalNonAssocSemiringstatement and proof · cited by 10
- DirectSum.gMulHomstatement and proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- DirectSum.mul_eq_dfinsuppSumproof · cited by 3
- DirectSum.mulHom_of_ofproof · cited by 1