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Theorems · Definition · algebraic geometry

AlgebraicGeometry.presentationTilde

{R : CommRingCat} →
  (M : ModuleCat ↑R) →
    (s : Set ↑M) →
      Submodule.span (↑R) s = ⊤ →
        (t : Set (↑s →₀ ↑R)) →
          Submodule.span (↑R) t = (Finsupp.linearCombination (↑R) Subtype.val).ker →
            SheafOfModules.Presentation (AlgebraicGeometry.tilde M)

Given a presentation of a module M, we may construct an associated presentation of M^~.

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Mathlib.AlgebraicGeometry.Modules.Tilde
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Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetCategoryTheory.Functor.obj · cited by 19642Functor.objRingHom.id · cited by 18349RingHom.idCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorTop.top · cited by 9680Top.topCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Iso.hom · cited by 7684Iso.homSubmodule · cited by 7192SubmoduleSet.Elem · cited by 7166Set.ElemCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso.inv · cited by 6514Iso.invFinsupp · cited by 5255FinsuppAddMonoidHom · cited by 3230AddMonoidHomAlgebraicGeometry.presentatio…CITED BYCITES

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