Theorems · Theorem · category theory

CategoryTheory.rightExactFunctor_le_additiveFunctor

∀ (C : Type u₁) (D : Type u₂) [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.Preadditive C] [inst_3 : CategoryTheory.Preadditive D]
  [CategoryTheory.Limits.HasZeroObject C] [CategoryTheory.Limits.HasZeroObject D]
  [CategoryTheory.Limits.HasBinaryBiproducts C],
  CategoryTheory.rightExactFunctor C D ≤ CategoryTheory.additiveFunctor C D

Defined in: Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
Cited by: 0 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Preadditive CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasBinaryBiproducts

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Cites9

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.Functorstatement and proof · cited by 16,252
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.ObjectPropertystatement · cited by 798
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CategoryTheory.rightExactFunctorstatement and proof · cited by 18
CategoryTheory.additiveFunctorstatement · cited by 15
CategoryTheory.Functor.additive_of_preservesBinaryBiproductsproof · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.AdditiveFunctor.ofRightExactproof · cited by 2