Theorems · Definition · ring theory
NonUnitalSubring.comap
{F : Type w} →
{R : Type u} →
{S : Type v} →
[inst : NonUnitalNonAssocRing R] →
[inst_1 : NonUnitalNonAssocRing S] →
[inst_2 : FunLike F R S] → [NonUnitalRingHomClass F R S] → F → NonUnitalSubring S → NonUnitalSubring RThe preimage of a NonUnitalSubring along a ring homomorphism is a NonUnitalSubring.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.preimageproof · cited by 4,946
- AddSubgroupproof · cited by 3,232
- FunLikestatement and proof · cited by 2,560
- NonUnitalNonAssocRingstatement and proof · cited by 354
- Subsemigroupproof · cited by 323
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
- AddSubsemigroup.carrierproof · cited by 198
- NonUnitalSubringstatement and proof · cited by 185
- AddSubgroup.comapproof · cited by 123
- NonUnitalRingHomClassstatement and proof · cited by 82
Cited by15
Results whose statement or proof uses this declaration.
- NonUnitalSubring.gc_map_comapstatement · cited by 7
- NonUnitalSubring.mem_comapstatement · cited by 2
- NonUnitalSubring.comap_topstatement · cited by 1
- NonUnitalSubring.map_equiv_eq_comap_symmstatement and proof · cited by 1
- NonUnitalSubring.map_le_iff_le_comapstatement · cited by 1
- NonUnitalSubring.top_prodstatement · cited by 1
- NonUnitalSubring.comap.congr_simpstatement and proof · cited by 0
- NonUnitalSubring.closure_preimage_lestatement · cited by 0
- NonUnitalRingHom.closure_preimage_lestatement · cited by 0
- NonUnitalSubring.coe_comapstatement · cited by 0
- NonUnitalSubring.prod_topstatement · cited by 0
- NonUnitalSubring.comap_comapstatement · cited by 0