Mathlib Map

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 R

The preimage of a NonUnitalSubring along a ring homomorphism is a NonUnitalSubring.

Defined in
Mathlib.RingTheory.NonUnitalSubring.Basic
Cited by
15 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext
Assumes
NonUnitalNonAssocRingNonUnitalNonAssocRingFunLikeNonUnitalRingHomClass

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NonUnitalSubring.gc_map_comap · cited by 7NonUnitalSubring.gc_map_c…NonUnitalSubring.mem_comap · cited by 2NonUnitalSubring.mem_comapNonUnitalSubring.comap_top · cited by 1NonUnitalSubring.comap_topNonUnitalSubring.map_equiv_eq_comap_symm · cited by 1NonUnitalSubring.map_equi…NonUnitalSubring.map_le_iff_le_comap · cited by 1NonUnitalSubring.map_le_i…NonUnitalSubring.top_prod · cited by 1NonUnitalSubring.top_prodNonUnitalSubring.comap.congr_simp · cited by 0comap.congr_simpNonUnitalSubring.closure_preimage_le · cited by 0NonUnitalSubring.closure_…NonUnitalRingHom.closure_preimage_le · cited by 0NonUnitalRingHom.closure_…NonUnitalSubring.coe_comap · cited by 0NonUnitalSubring.coe_comapNonUnitalSubring.prod_top · cited by 0NonUnitalSubring.prod_topNonUnitalSubring.comap_comap · cited by 0NonUnitalSubring.comap_co…NonUnitalSubring.comap_equiv_eq_map_symm · cited by 0NonUnitalSubring.comap_eq…NonUnitalSubring.comap_iInf · cited by 0NonUnitalSubring.comap_iI…NonUnitalSubring.comap_inf · cited by 0NonUnitalSubring.comap_infDFunLike.coe · cited by 62936DFunLike.coeSet.preimage · cited by 4946Set.preimageAddSubgroup · cited by 3232AddSubgroupFunLike · cited by 2560FunLikeNonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingSubsemigroup · cited by 323SubsemigroupAddMonoidHomClass.toAddMonoidHom · cited by 232AddMonoidHomClass.toAddMo…AddSubmonoid.toAddSubsemigroup · cited by 198AddSubmonoid.toAddSubsemi…AddSubsemigroup.carrier · cited by 198AddSubsemigroup.carrierNonUnitalSubring · cited by 185NonUnitalSubringAddSubgroup.comap · cited by 123AddSubgroup.comapNonUnitalRingHomClass · cited by 82NonUnitalRingHomClassNonUnitalSubsemiring.toAddSubmonoid · cited by 56NonUnitalSubsemiring.toAd…Subsemigroup.comap · cited by 39Subsemigroup.comapMulHomClass.toMulHom · cited by 31MulHomClass.toMulHomNonUnitalSubring.comapCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.