Theorems · Theorem · group theory
addCommute_map_iff
∀ {F : Type u_1} {M : Type u_2} {N : Type u_3} [inst : Add M] [inst_1 : Add N] [inst_2 : FunLike F M N]
[AddHomClass F M N] {f : F}, Function.Injective ⇑f → ∀ {x y : M}, AddCommute (f x) (f y) ↔ AddCommute x y- Defined in
- Mathlib.Algebra.Group.Commute.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddAddFunLikeAddHomClass
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
- FunLikestatement and proof · cited by 2,560
- AddCommutestatement and proof · cited by 185
- AddHomClassstatement and proof · cited by 65
- AddCommute.mapproof · cited by 9
- AddCommute.of_mapproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.