Theorems · Theorem · category theory
Module.Flat.rTensor_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
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingModule.Flat
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- Module.Flatstatement and proof · cited by 279
- CategoryTheory.ShortComplex.mapstatement and proof · cited by 188
- CategoryTheory.MonoidalCategory.curriedTensorstatement · cited by 170
- CategoryTheory.MonoidalCategory.tensorRightstatement and proof · cited by 119
- CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exactproof · cited by 11
- Module.Flat.rTensor_exactproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Module.Flat.iff_rTensor_preserves_shortComplex_exactproof · cited by 0