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Theorems · Definition · category theory

CategoryTheory.ChosenPullbacksAlong.pullback

{C : Type u₁} →
  {inst : CategoryTheory.Category.{v₁, u₁} C} →
    {Y X : C} →
      (f : Y ⟶ X) →
        [self : CategoryTheory.ChosenPullbacksAlong f] →
          CategoryTheory.Functor (CategoryTheory.Over X) (CategoryTheory.Over Y)

The pullback functor along f.

Defined in
Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong
Cited by
62 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.ChosenPullbacksAlong

Around this declaration

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

CategoryTheory.ChosenPullbacksAlong.snd · cited by 45ChosenPullbacksAlong.sndCategoryTheory.ChosenPullbacksAlong.pullbackObj · cited by 42ChosenPullbacksAlong.pull…CategoryTheory.ChosenPullbacksAlong.mapPullbackAdj · cited by 29ChosenPullbacksAlong.mapP…CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj · cited by 16ExponentiableMorphism.pul…CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback · cited by 8ChosenPullbacksAlong.pull…CategoryTheory.ExponentiableMorphism.coev · cited by 7ExponentiableMorphism.coevCategoryTheory.ExponentiableMorphism.ev · cited by 7ExponentiableMorphism.evCategoryTheory.ChosenPullbacksAlong.pullbackId · cited by 6ChosenPullbacksAlong.pull…CategoryTheory.ChosenPullbacksAlong.hom_ext · cited by 5ChosenPullbacksAlong.hom_…CategoryTheory.ChosenPullbacksAlong.comp · cited by 4ChosenPullbacksAlong.compCategoryTheory.ChosenPullbacksAlong.fst' · cited by 4ChosenPullbacksAlong.fst'CategoryTheory.ChosenPullbacksAlong.lift_fst · cited by 4ChosenPullbacksAlong.lift…CategoryTheory.ChosenPullbacksAlong.pullbackComp · cited by 4ChosenPullbacksAlong.pull…CategoryTheory.ExponentiableMorphism.pushforwardCurry · cited by 3ExponentiableMorphism.pus…CategoryTheory.ExponentiableMorphism.pushforwardUncurry · cited by 3ExponentiableMorphism.pus…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.ChosenPullbacksAlong · cited by 73CategoryTheory.ChosenPull…ChosenPullbacksAlong.pullbackCITED BYCITES

Cites5

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Cited by85

Results whose statement or proof uses this declaration.