Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.pullback.snd

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Z) →
        (g : Y ⟶ Z) → [inst_1 : CategoryTheory.Limits.HasPullback f g] → CategoryTheory.Limits.pullback f g ⟶ Y

The second projection of the pullback of f and g.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by
637 results in Mathlib
Foundations
Depth 24 from the axioms, rests on 150 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullback

Around this declaration

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

CategoryTheory.Limits.pullback.map · cited by 156pullback.mapCategoryTheory.Limits.pullback.condition · cited by 122pullback.conditionAlgebraicGeometry.morphismRestrict · cited by 90AlgebraicGeometry.morphis…CategoryTheory.IsPullback.of_hasPullback · cited by 70IsPullback.of_hasPullbackCategoryTheory.Limits.pullback.hom_ext · cited by 63pullback.hom_extCategoryTheory.Over.pullback · cited by 53Over.pullbackCategoryTheory.MorphismProperty.Over.pullback · cited by 42Over.pullbackAlgebraicGeometry.Scheme.Cover.pullbackHom · cited by 32Cover.pullbackHomCategoryTheory.Limits.pullback.lift_snd · cited by 30pullback.lift_sndAlgebraicGeometry.morphismRestrict_ι · cited by 25AlgebraicGeometry.morphis…CategoryTheory.Limits.pullback.condition_assoc · cited by 24pullback.condition_assocCategoryTheory.Limits.pullbackAssoc · cited by 23Limits.pullbackAssocCategoryTheory.PreZeroHypercover.toPreOneHypercover · cited by 23PreZeroHypercover.toPreOn…CategoryTheory.Limits.hasPullback_symmetry · cited by 22Limits.hasPullback_symmet…CategoryTheory.Functor.PullbackObjObj.ofHasPullback · cited by 21PullbackObjObj.ofHasPullb…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.cospan · cited by 467Limits.cospanCategoryTheory.Limits.HasPullback · cited by 434Limits.HasPullbackCategoryTheory.Limits.limit.π · cited by 278limit.πCategoryTheory.Limits.WalkingCospan.right · cited by 182WalkingCospan.rightpullback.sndCITED BYCITES

Cites7

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Cited by741

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 741.