Theorems · Theorem · group theory
DirectSum.map_apply
∀ {ι : Type u_3} {α : ι → Type u_4} {β : ι → Type u_5} [inst : (i : ι) → AddCommMonoid (α i)]
[inst_1 : (i : ι) → AddCommMonoid (β i)] (f : (i : ι) → α i →+ β i) (i : ι) (x : DirectSum ι fun i => α i),
((DirectSum.map f) x) i = (f i) (x i)- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 3,230
- map_zeroproof · cited by 1,614
- DFinsuppstatement · cited by 694
- DirectSumstatement and proof · cited by 446
- DirectSum.mapstatement · cited by 15
- DFinsupp.mapRange_applyproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- map_directSumDecomposeproof · cited by 1
- DirectSum.map_eq_iffproof · cited by 1