Theorems · Definition · commutative algebra
RingCon.congr
{M : Type u_1} →
{N : Type u_2} →
[inst : NonAssocSemiring M] →
[inst_1 : NonAssocSemiring N] →
{c : RingCon M} → {d : RingCon N} → (e : M ≃+* N) → c = d.comap e → c.Quotient ≃+* d.QuotientAn isomorphism of rings e : M ≃+* N generates an isomorphism between quotient spaces,
if it is compatible with the relations.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- RingEquivstatement and proof · cited by 1,147
- NonAssocSemiringstatement and proof · cited by 805
- RingConstatement and proof · cited by 219
- EquivLike.toEquivproof · cited by 125
- RingCon.Quotientstatement · cited by 118
- Con.toSetoidproof · cited by 38
- RingCon.toConproof · cited by 36
- RingCon.comapstatement and proof · cited by 32
- Quotient.congrproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- RingCon.comapQuotientEquivOfSurjproof · cited by 3
- RingCon.comapQuotientEquivRangeSproof · cited by 3
- RingCon.congrₐproof · cited by 2
- RingCon.congr.congr_simpstatement and proof · cited by 0
- RingCon.congr_mkstatement · cited by 0
- RingCon.congr_symmstatement · cited by 0