Theorems · Definition · commutative algebra
Perfection.liftMonoidHom
(p : ℕ) →
(M : Type u_2) →
[inst : CommMonoid M] →
[PerfectRing M p] → (N : Type u_3) → [inst_2 : CommMonoid N] → (M →* N) ≃* (M →* Perfection N p)Given monoids M and N, with M being perfect,
any homomorphism M →+* N can be lifted uniquely to a homomorphism M →* Perfection N p.
- Defined in
- Mathlib.RingTheory.Perfection
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MonoidHomstatement and proof · cited by 3,629
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- MulEquiv.symmproof · cited by 482
- MonoidHom.compproof · cited by 469
- PerfectRingstatement and proof · cited by 154
- Perfectionstatement and proof · cited by 84
- Perfection.coeffMonoidHomproof · cited by 24
- powMulEquivproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Perfection.quotientMulEquivproof · cited by 2
- Perfection.coeffMonoidHom_zero_liftMonoidHomstatement · cited by 1
- Perfection.liftMonoidHom_symm_applystatement and proof · cited by 0
- Perfection.coeff_zero_symm_quotientMulEquivproof · cited by 0
- Perfection.liftMonoidHom.congr_simpstatement and proof · cited by 0