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feat(AlgebraicGeometry/Modules): flat sheaves of modules #2

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feat(AlgebraicGeometry/Modules): flat sheaves of modules
chrisflav-agent[bot] Jun 27, 2026
c7f79b6
refactor(AlgebraicGeometry/Modules): deduce flat_tilde_iff from flat_…
chrisflav Jun 27, 2026
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1 change: 1 addition & 0 deletions Mathlib.lean
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Expand Up @@ -1396,6 +1396,7 @@ public import Mathlib.AlgebraicGeometry.IdealSheaf.IrreducibleComponent
public import Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme
public import Mathlib.AlgebraicGeometry.Limits
public import Mathlib.AlgebraicGeometry.LimitsOver
public import Mathlib.AlgebraicGeometry.Modules.Flat
public import Mathlib.AlgebraicGeometry.Modules.Presheaf
public import Mathlib.AlgebraicGeometry.Modules.Sheaf
public import Mathlib.AlgebraicGeometry.Modules.Tilde
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5 changes: 4 additions & 1 deletion Mathlib/Algebra/Module/RingHom.lean
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Expand Up @@ -60,9 +60,12 @@ abbrev Module.compHom [Semiring S] (f : S →+* R) : Module S M :=
-- Somehow, now that `SMul` is heterogeneous, it can't unfold earlier fields of a definition for
-- use in later fields. See
-- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Heterogeneous.20scalar.20multiplication
-- TODO(jmc): there should be a rw-lemma `smul_comp` close to `SMulZeroClass.compFun`
add_smul := fun r s x => show f (r + s) • x = f r • x + f s • x by simp [add_smul] }

lemma Module.compHom_smul [Semiring S] (f : S →+* R) (s : S) (m : M) :
letI := Module.compHom M f; s • m = f s • m :=
rfl

end AddCommMonoid

/-- A ring homomorphism `f : R →+* M` defines a module structure by `r • x = f r * x`.
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