Theorems · Theorem · commutative algebra
AdicCompletion.map_ext
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Sort u_6} {f g : AdicCompletion I M → N},
(∀ (a : AdicCompletion.AdicCauchySequence I M), f ((AdicCompletion.mk I M) a) = g ((AdicCompletion.mk I M) a)) → f = gEquality of maps out of an adic completion can be checked on Cauchy sequences.
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- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- AdicCompletionstatement and proof · cited by 160
- AdicCompletion.AdicCauchySequencestatement and proof · cited by 41
- AdicCompletion.mkstatement and proof · cited by 22
- AdicCompletion.induction_onproof · cited by 9
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