Theorems · Theorem · category theory

Module.Flat.iff_rTensor_preserves_shortComplex_exact

∀ {R : Type u} [inst : CommRing R] (M : ModuleCat R),
  Module.Flat R ↑M ↔
    ∀ (C : CategoryTheory.ShortComplex (ModuleCat R)),
      C.Exact → (C.map (CategoryTheory.MonoidalCategory.tensorRight M)).Exact

Defined in: Mathlib.RingTheory.Flat.CategoryTheory
Cited by: 0 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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DFunLike.coeproof · cited by 62,936
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CategoryTheory.ShortComplexstatement and proof · cited by 1,850
ModuleCatstatement and proof · cited by 1,429
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ModuleCat.Hom.homproof · cited by 341

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