Theorems · Definition · group theory
Subsemigroup.giMapComap
{M : Type u_1} →
{N : Type u_2} →
[inst : Mul M] →
[inst_1 : Mul N] →
{f : M →ₙ* N} → Function.Surjective ⇑f → GaloisInsertion (Subsemigroup.map f) (Subsemigroup.comap f)map f and comap f form a GaloisInsertion when f is surjective.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, 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
- Subsemigroupstatement · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.mapstatement · cited by 51
- Subsemigroup.comapstatement · cited by 39
- GaloisInsertionstatement · cited by 35
- Subsemigroup.gc_map_comapproof · cited by 15
- GaloisConnection.toGaloisInsertionproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- Subsemigroup.map_iInf_comap_of_surjectiveproof · cited by 0
- Subsemigroup.comap_injective_of_surjectiveproof · cited by 0
- Subsemigroup.comap_le_comap_iff_of_surjectiveproof · cited by 0
- Subsemigroup.map_iSup_comap_of_surjectiveproof · cited by 0
- Subsemigroup.comap_strictMono_of_surjectiveproof · cited by 0
- Subsemigroup.map_inf_comap_of_surjectiveproof · cited by 0
- Subsemigroup.map_sup_comap_of_surjectiveproof · cited by 0
- Subsemigroup.map_surjective_of_surjectiveproof · cited by 0
- Subsemigroup.map_comap_eq_of_surjectiveproof · cited by 0