Theorems · Definition · commutative algebra
FreeCommRing.lift
{α : Type u} → {R : Type v} → [inst : CommRing R] → (α → R) ≃ (FreeCommRing α →+* R)Lift a map α → R to an additive group homomorphism FreeCommRing α → R.
- Defined in
- Mathlib.RingTheory.FreeCommRing
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Equivstatement · cited by 8,337
- Equiv.transproof · cited by 337
- FreeCommRingstatement · cited by 43
- FreeAbelianGroup.liftMonoidproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- FreeCommRing.lift_ofstatement · cited by 9
- Ring.DirectLimit.liftproof · cited by 6
- FirstOrder.Ring.realize_termOfFreeCommRingstatement and proof · cited by 5
- FreeCommRing.hom_extproof · cited by 3
- FreeCommRing.mapproof · cited by 2
- FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realizeproof · cited by 2
- FreeCommRing.restrictionproof · cited by 2
- FirstOrder.Ring.lift_genericPolyMapstatement and proof · cited by 2
- CommRingCat.Limits.isUnit_iff_forall_isUnitproof · cited by 1
- FreeCommRing.isSupported_ofproof · cited by 1
- FirstOrder.Field.lift_genericMonicPolystatement and proof · cited by 1
- freeCommRingEquivMvPolynomialIntproof · cited by 0