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Theorems · Definition · commutative algebra

CommRing.Pic.mk

(R : Type u) →
  (M : Type v) →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → [Module.Invertible R M] → CommRing.Pic R

The class of an invertible module in the Picard group.

Defined in
Mathlib.RingTheory.PicardGroup
Cited by
17 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoidModuleModule.Invertible

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CommRing.Pic.mapAlgebra · cited by 10Pic.mapAlgebraSubmodule.unitsToPic · cited by 10Submodule.unitsToPicCommRing.Pic.mk_eq_iff · cited by 5Pic.mk_eq_iffCommRing.Pic.mk_eq_self · cited by 5Pic.mk_eq_selfCommRing.Pic.mk_eq_one_iff · cited by 4Pic.mk_eq_one_iffCommRing.Pic.mk.linearEquiv · cited by 3mk.linearEquivCommRing.Pic.mk_eq_mk_iff · cited by 3Pic.mk_eq_mk_iffCommRing.Pic.mk_eq_one_iff_free · cited by 2Pic.mk_eq_one_iff_freeCommRing.Pic.mk_tensor · cited by 2Pic.mk_tensorCommRing.Pic.mk_dual · cited by 1Pic.mk_dualCommRing.Pic.mk_self · cited by 1Pic.mk_selfCommRing.Pic.subsingleton_iffₛ · cited by 1Pic.subsingleton_iffₛCommRing.Pic.mk.congr_simp · cited by 0mk.congr_simpIdeal.eq_top_of_mk_tensor_eq_one · cited by 0Ideal.eq_top_of_mk_tensor…CommRing.Pic.inv_eq_dual · cited by 0Pic.inv_eq_dualDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringUnits · cited by 2804UnitsModule.Dual · cited by 583Module.DualequivShrink · cited by 118equivShrinkSemimoduleCat · cited by 108SemimoduleCatModule.Invertible · cited by 41Module.InvertibleCommRing.Pic · cited by 37CommRing.PicCategoryTheory.Skeleton · cited by 35CategoryTheory.SkeletonSemimoduleCat.of · cited by 25SemimoduleCat.ofCategoryTheory.isIsomorphicSetoid · cited by 24CategoryTheory.isIsomorph…Units.mkOfMulEqOne · cited by 15Units.mkOfMulEqOneModule.Finite.reprₛ · cited by 2Finite.reprₛPic.mkCITED BYCITES

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.