Theorems · Theorem · group theory
MonoidHom.mrange_eq_top_of_surjective
∀ {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), Function.Surjective ⇑f → MonoidHom.mrange f = ⊤The range of a surjective MonoidHom is the whole of the codomain.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Top.topstatement · cited by 9,680
- 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
- MonoidHom.mrangestatement · cited by 63
- MonoidHom.mrange_eq_topproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Monoid.fg_iff_exists_freeMonoid_hom_surjectiveproof · cited by 1
- Submonoid.mrange_sndproof · cited by 1
- Submonoid.mrange_fstproof · cited by 1
- Submonoid.codisjoint_mapproof · cited by 0
- Submonoid.map_comap_eq_self_of_surjectiveproof · cited by 0
- Monoid.Coprod.mrange_swapproof · cited by 0