Theorems · Theorem · category theory
Module.Flat.iff_preservesFiniteLimits_tensorRight
∀ {R : Type u} [inst : CommRing R] (M : ModuleCat R),
Module.Flat R ↑M ↔ CategoryTheory.Limits.PreservesFiniteLimits (CategoryTheory.MonoidalCategory.tensorRight M)- Defined in
- Mathlib.RingTheory.Flat.CategoryTheory
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites10
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
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- CategoryTheory.Iso.symmproof · cited by 993
- Module.Flatstatement and proof · cited by 279
- CategoryTheory.Limits.PreservesFiniteLimitsstatement and proof · cited by 121
- CategoryTheory.MonoidalCategory.tensorRightstatement and proof · cited by 119
- CategoryTheory.BraidedCategory.tensorLeftIsoTensorRightproof · cited by 5
- CategoryTheory.Limits.preservesFiniteLimits_of_natIsoproof · cited by 4
- Module.Flat.iff_preservesFiniteLimits_tensorLeftproof · cited by 1
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