Theorems · Theorem · group theory
Submonoid.map_comap_eq_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 → ∀ (S : Submonoid N), Submonoid.map f (Submonoid.comap f S) = S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement · cited by 190
- Submonoid.comapstatement · cited by 179
- GaloisInsertion.l_u_eqproof · cited by 37
- Submonoid.giMapComapproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.surjective_localRingHom_of_surjectiveproof · cited by 0