Theorems · Definition · category theory
CategoryTheory.exactFunctor
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(D : Type u₂) →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.ObjectProperty (CategoryTheory.Functor C D)Exactness, as a property of objects in C ⥤ D.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 16,252
- CategoryTheory.ObjectPropertystatement · cited by 798
- CategoryTheory.leftExactFunctorproof · cited by 25
- CategoryTheory.rightExactFunctorproof · cited by 18
Cited by32
Results whose statement or proof uses this declaration.
- CategoryTheory.ExactFunctorproof · cited by 17
- CategoryTheory.ExactFunctor.forgetstatement and proof · cited by 7
- CategoryTheory.ExactFunctor.whiskeringLeftstatement and proof · cited by 3
- CategoryTheory.ExactFunctor.whiskeringRightstatement and proof · cited by 3
- CategoryTheory.RightExactFunctor.ofExactstatement · cited by 2
- CategoryTheory.AdditiveFunctor.ofExactstatement · cited by 2
- CategoryTheory.ObjectProperty.SerreClassLocalization.whiskeringLeftstatement and proof · cited by 2
- CategoryTheory.LeftExactFunctor.ofExactstatement · cited by 2
- CategoryTheory.ObjectProperty.SerreClassLocalization.exactFunctor_comp_iffstatement · cited by 1
- CategoryTheory.exactFunctor_le_leftExactFunctorstatement and proof · cited by 1
- CategoryTheory.RightExactFunctor.ofExact_map_homstatement · cited by 0
- CategoryTheory.RightExactFunctor.ofExact_objstatement · cited by 0