Theorems · Theorem · commutative algebra
AdicCompletion.map_mk
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Type u_3} [inst_3 : AddCommGroup N] [inst_4 : Module R N] (f : M →ₗ[R] N)
(a : AdicCompletion.AdicCauchySequence I M),
(AdicCompletion.map I f) ((AdicCompletion.mk I M) a) =
(AdicCompletion.mk I N) ((AdicCompletion.AdicCauchySequence.map I f) a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Idealstatement and proof · cited by 4,748
- AdicCompletionstatement · cited by 160
- AdicCompletion.AdicCauchySequencestatement and proof · cited by 41
- AdicCompletion.mapstatement · cited by 24
- AdicCompletion.mkstatement · cited by 22
- AdicCompletion.AdicCauchySequence.mapstatement · cited by 11
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