Theorems · Theorem · group theory
MonoidHom.mrange_eq_top
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {F : Type u_4} [inst_2 : FunLike F M N]
[mc : MonoidHomClass F M N] {f : F}, MonoidHom.mrange f = ⊤ ↔ Function.Surjective ⇑f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- Submonoidstatement · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassstatement and proof · cited by 244
- SetLike.ext'_iffproof · cited by 78
- MonoidHom.mrangestatement · cited by 63
Cited by4
Results whose statement or proof uses this declaration.
- MonoidHom.mrange_eq_top_of_surjectiveproof · cited by 6
- Monoid.fg_of_surjectiveproof · cited by 4
- Monoid.fg_iff_exists_freeMonoid_hom_surjectiveproof · cited by 1
- Con.mrange_mk'proof · cited by 1