Theorems · Definition · commutative algebra
CommRing.Pic.AsModule
{R : Type u} → [inst : CommSemiring R] → CommRing.Pic R → Type uA representative of an element in the Picard group.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Equiv.symmproof · cited by 3,681
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Quotient.outproof · cited by 141
- equivShrinkproof · cited by 118
- SemimoduleCatproof · cited by 108
- SemimoduleCat.carrierproof · cited by 87
- CommRing.Picstatement and proof · cited by 37
- CategoryTheory.Skeletonproof · cited by 35
Cited by14
Results whose statement or proof uses this declaration.
- CommRing.Pic.mapAlgebraproof · cited by 10
- CommRing.Pic.mk_eq_iffstatement and proof · cited by 5
- CommRing.Pic.mk_eq_selfstatement and proof · cited by 5
- Submodule.range_unitsToPicproof · cited by 4
- CommRing.Pic.mk.linearEquivstatement · cited by 3
- CommRing.Pic.mk_eq_mk_iffproof · cited by 3
- CommRing.Pic.mapAlgebra_mapAlgebraproof · cited by 1
- CommRing.Pic.mapAlgebra_self_applyproof · cited by 1
- CommRing.Pic.subsingleton_iffₛproof · cited by 1
- Submodule.unitsToPicEquivstatement · cited by 1
- CommRing.Pic.mul_eq_tensorstatement and proof · cited by 0
- CommRing.Pic.ext_iffstatement · cited by 0