Theorems · Definition · group theory
Subsemigroup.gciMapComap
{M : Type u_1} →
{N : Type u_2} →
[inst : Mul M] →
[inst_1 : Mul N] →
{f : M →ₙ* N} → Function.Injective ⇑f → GaloisCoinsertion (Subsemigroup.map f) (Subsemigroup.comap f)map f and comap f form a GaloisCoinsertion when f is injective.
- 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 and proof · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.mapstatement · cited by 51
- Subsemigroup.comapstatement · cited by 39
- GaloisCoinsertionstatement · cited by 35
- Subsemigroup.gc_map_comapproof · cited by 15
- GaloisConnection.toGaloisCoinsertionproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- Subsemigroup.comap_inf_map_of_injectiveproof · cited by 0
- Subsemigroup.comap_map_eq_of_injectiveproof · cited by 0
- Subsemigroup.comap_sup_map_of_injectiveproof · cited by 0
- Subsemigroup.comap_surjective_of_injectiveproof · cited by 0
- Subsemigroup.map_injective_of_injectiveproof · cited by 0
- Subsemigroup.map_le_map_iff_of_injectiveproof · cited by 0
- Subsemigroup.map_strictMono_of_injectiveproof · cited by 0
- Subsemigroup.comap_iInf_map_of_injectiveproof · cited by 0
- Subsemigroup.comap_iSup_map_of_injectiveproof · cited by 0