Theorems · Theorem · category theory
CategoryTheory.isZero_Tor_succ_of_projective
∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.MonoidalPreadditive C]
[inst_4 : CategoryTheory.HasProjectiveResolutions C] (X Y : C) [CategoryTheory.Projective Y] (n : ℕ),
CategoryTheory.Limits.IsZero (((CategoryTheory.Tor C (n + 1)).obj X).obj Y)The higher Tor groups for X and Y are zero if Y is projective.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Tor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Limits.IsZerostatement · cited by 306
- CategoryTheory.Projectivestatement and proof · cited by 78
- CategoryTheory.MonoidalPreadditivestatement and proof · cited by 65
- CategoryTheory.HasProjectiveResolutionsstatement and proof · cited by 42
- CategoryTheory.MonoidalCategory.tensoringLeftproof · cited by 9
- CategoryTheory.Torstatement · cited by 3
- CategoryTheory.Functor.isZero_leftDerived_obj_projective_succproof · cited by 3
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