Theorems · Theorem · category theory
CategoryTheory.Tor_map
∀ (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] (n : ℕ) {X Y : C} (f : X ⟶ Y),
(CategoryTheory.Tor C n).map f =
CategoryTheory.NatTrans.leftDerived ((CategoryTheory.MonoidalCategory.tensoringLeft C).map f) n- 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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Cites13
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · 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.leftDerivedstatement · cited by 29
- CategoryTheory.MonoidalCategory.tensoringLeftstatement · cited by 9
- CategoryTheory.NatTrans.leftDerivedstatement · cited by 8
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