Theorems · Definition · commutative algebra
Algebra.codRestrictEqLocusPushoutCocone
(R S : Type u) →
[inst : CommRing R] →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] →
R →+*
↑(CommRingCat.equalizerFork (CommRingCat.pushoutCocone R S S).inl (CommRingCat.pushoutCocone R S S).inr).ptThe canonical ring map from R to the explicit equalizer of
includeLeft : S ⟶ S ⊗[R] S and includeRight : S ⟶ S ⊗[R] S.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- CommRingCatstatement · cited by 2,333
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
- CategoryTheory.Limits.parallelPairstatement · cited by 766
- CommRingCat.Hom.homproof · cited by 432
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.codRestrictEqLocusPushoutCocone.surjective_of_isEffectivestatement and proof · cited by 1
- Algebra.codRestrictEqLocusPushoutCocone.injective_of_faithfulSMulstatement · cited by 1
- CommRingCat.isLimitForkPushoutSelfOfFaithfullyFlatproof · cited by 0
- Algebra.codRestrictEqLocusPushoutCocone.bijective_of_faithfullyFlatstatement · cited by 0