Theorems · Theorem · commutative algebra
Algebra.codRestrictEqLocusPushoutCocone.injective_of_faithfulSMul
∀ (R S : Type u) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [FaithfulSMul R S], Function.Injective ⇑(Algebra.codRestrictEqLocusPushoutCocone R S)
Injectivity of algebraMap R S implies injectivity of codRestrictEqLocusPushoutCocone.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · 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
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.codRestrictEqLocusPushoutCocone.bijective_of_faithfullyFlatproof · cited by 0