Theorems · Theorem · category theory
LinearMap.exact_zero_iff_injective
∀ {R : Type u_8} [inst : Ring R] {M : Type u_12} {N : Type u_13} (P : Type u_14) [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : AddCommMonoid P] [inst_4 : Module R N] [inst_5 : Module R M] [inst_6 : Module R P]
(f : M →ₗ[R] N), Function.Exact ⇑0 ⇑f ↔ Function.Injective ⇑f- Defined in
- Mathlib.Algebra.Exact.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Bot.botproof · cited by 4,720
- LinearMap.kerproof · cited by 848
- Function.Exactstatement · cited by 182
- LinearMap.range_zeroproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Module.FaithfullyFlat.lTensor_injective_iff_injectiveproof · cited by 4
- Algebra.Extension.tensorToH1Cotangent_bijective_of_flatproof · cited by 0