Theorems · Definition · category theory

CategoryTheory.Tor

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.Abelian C] →
        [CategoryTheory.MonoidalPreadditive C] →
          [CategoryTheory.HasProjectiveResolutions C] → ℕ → CategoryTheory.Functor C (CategoryTheory.Functor C C)

We define Tor C n : C ⥤ C ⥤ C by left-deriving in the second factor of (X, Y) ↦ X ⊗ Y.

Defined in: Mathlib.CategoryTheory.Monoidal.Tor
Cited by: 3 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.Abelian CategoryTheory.MonoidalPreadditive CategoryTheory.HasProjectiveResolutions

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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.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homproof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.mapproof · cited by 8,698
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.MonoidalPreadditivestatement and proof · cited by 65
CategoryTheory.HasProjectiveResolutionsstatement and proof · cited by 42
CategoryTheory.Functor.leftDerivedproof · cited by 29
CategoryTheory.MonoidalCategory.tensoringLeftproof · cited by 9
CategoryTheory.NatTrans.leftDerivedproof · cited by 8

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.isZero_Tor_succ_of_projectivestatement · cited by 0
CategoryTheory.Tor_mapstatement and proof · cited by 0
CategoryTheory.Tor_objstatement and proof · cited by 0