Theorems · Definition · commutative algebra
CommRing.Pic.mapRingHom
{R : Type u} →
[inst : CommSemiring R] → {S : Type u_7} → [inst_1 : CommSemiring S] → (R →+* S) → CommRing.Pic R →* CommRing.Pic SEvery ring homomorphism between commutative semirings induces a homomorphism between Picard groups.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebraproof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- MonoidHomstatement · cited by 3,629
- RingHom.toAlgebraproof · cited by 337
- CommRing.Picstatement · cited by 37
- CommRing.Pic.mapAlgebraproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- CommRing.Pic.mapRingHom_comp_mapRingHomstatement · cited by 1
- CommRing.Pic.mapRingHom_idstatement · cited by 1
- CommRing.Pic.mapRingHom_algebraMapstatement · cited by 0
- CommRing.Pic.mapRingHom_id_applystatement · cited by 0
- CommRing.Pic.mapRingHom_mapRingHomstatement · cited by 0
- CommRing.Pic.functorproof · cited by 0