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Theorems · Definition · category theory

CategoryTheory.rightExactFunctor

(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)

Right-exactness, as a property of objects in C ⥤ D.

Defined in
Mathlib.CategoryTheory.Limits.ExactFunctor
Cited by
18 results in Mathlib
Foundations
Depth 20 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 23CategoryTheory.exactFunct…CategoryTheory.RightExactFunctor · cited by 13CategoryTheory.RightExact…CategoryTheory.RightExactFunctor.forget · cited by 7RightExactFunctor.forgetCategoryTheory.RightExactFunctor.whiskeringLeft · cited by 3RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.whiskeringRight · cited by 3RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.ofExact · cited by 2RightExactFunctor.ofExactCategoryTheory.AdditiveFunctor.ofRightExact · cited by 2AdditiveFunctor.ofRightEx…CategoryTheory.RightExactFunctor.ofExact_map_hom · cited by 0RightExactFunctor.ofExact…CategoryTheory.RightExactFunctor.ofExact_obj · cited by 0RightExactFunctor.ofExact…CategoryTheory.RightExactFunctor.of_fst · cited by 0RightExactFunctor.of_fstCategoryTheory.RightExactFunctor.whiskeringLeft_map_app · cited by 0RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.whiskeringLeft_obj_map · cited by 0RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.whiskeringLeft_obj_obj_obj · cited by 0RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.whiskeringRight_map_app · cited by 0RightExactFunctor.whisker…CategoryTheory.RightExactFunctor.whiskeringRight_obj_map · cited by 0RightExactFunctor.whisker…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.Limits.PreservesFiniteColimits · cited by 102Limits.PreservesFiniteCol…CategoryTheory.rightExactFunc…CITED BYCITES

Cites4

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Cited by26

Results whose statement or proof uses this declaration.