Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Limits.hasPullback_symmetry_of_hasPullbacksAlong

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] {S X Y : C} {f : X ⟶ S}
  [CategoryTheory.Limits.HasPullbacksAlong f] {g : Y ⟶ S}, CategoryTheory.Limits.HasPullback f g
Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by
2 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlong
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.MorphismProperty.pullbackMap · cited by 1MorphismProperty.pullback…CategoryTheory.MorphismProperty.pullback_map · cited by 0MorphismProperty.pullback…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasPullback · cited by 434Limits.HasPullbackCategoryTheory.Limits.hasPullback_symmetry · cited by 22Limits.hasPullback_symmet…CategoryTheory.Limits.HasPullbacksAlong · cited by 21Limits.HasPullbacksAlongLimits.hasPullback_symmetry_o…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.