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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.

Defined in
Mathlib.CategoryTheory.Limits.ExactFunctor
Cited by
23 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ExactFunctor · cited by 17CategoryTheory.ExactFunct…CategoryTheory.ExactFunctor.forget · cited by 7ExactFunctor.forgetCategoryTheory.ExactFunctor.whiskeringLeft · cited by 3ExactFunctor.whiskeringLe…CategoryTheory.ExactFunctor.whiskeringRight · cited by 3ExactFunctor.whiskeringRi…CategoryTheory.RightExactFunctor.ofExact · cited by 2RightExactFunctor.ofExactCategoryTheory.AdditiveFunctor.ofExact · cited by 2AdditiveFunctor.ofExactCategoryTheory.ObjectProperty.SerreClassLocalization.whiskeringLeft · cited by 2SerreClassLocalization.wh…CategoryTheory.LeftExactFunctor.ofExact · cited by 2LeftExactFunctor.ofExactCategoryTheory.ObjectProperty.SerreClassLocalization.exactFunctor_comp_iff · cited by 1SerreClassLocalization.ex…CategoryTheory.exactFunctor_le_leftExactFunctor · cited by 1CategoryTheory.exactFunct…CategoryTheory.RightExactFunctor.ofExact_map_hom · cited by 0RightExactFunctor.ofExact…CategoryTheory.RightExactFunctor.ofExact_obj · cited by 0RightExactFunctor.ofExact…CategoryTheory.ExactFunctor.forget_map · cited by 0ExactFunctor.forget_mapCategoryTheory.ExactFunctor.forget_obj · cited by 0ExactFunctor.forget_objCategoryTheory.ExactFunctor.forget_obj_of · cited by 0ExactFunctor.forget_obj_ofCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.leftExactFunctor · cited by 25CategoryTheory.leftExactF…CategoryTheory.rightExactFunctor · cited by 18CategoryTheory.rightExact…CategoryTheory.exactFunctorCITED BYCITES

Cites5

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Cited by32

Results whose statement or proof uses this declaration.