Theorems · Definition · commutative algebra
AdicCompletion.AdicCauchySequence.map
{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] →
(M →ₗ[R] N) → AdicCompletion.AdicCauchySequence I M →ₗ[R] AdicCompletion.AdicCauchySequence I NA linear map induces a linear map on adic Cauchy sequences.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- AdicCompletion.AdicCauchySequencestatement and proof · cited by 41
Cited by11
Results whose statement or proof uses this declaration.
- AdicCompletion.AdicCauchySequence.map_apply_coestatement and proof · cited by 5
- AdicCompletion.map_injectiveproof · cited by 1
- AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
- AdicCompletion.map_mkstatement · cited by 0
- AdicCompletion.AdicCauchySequence.map_compstatement · cited by 0
- AdicCompletion.AdicCauchySequence.map_comp_applystatement · cited by 0
- AdicCompletion.AdicCauchySequence.map_idstatement · cited by 0
- AdicCompletion.AdicCauchySequence.map_zerostatement · cited by 0
- AdicCompletion.sumInv_comp_sumproof · cited by 0
- AdicCompletion.sum_comp_sumInvproof · cited by 0
- AdicCompletion.map_exactproof · cited by 0