Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong.of_isPullback

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {P : CategoryTheory.MorphismProperty C} {X Y : C} {f : X ⟶ Y}
  [self : P.IsStableUnderBaseChangeAlong f] {Z W : C} {f' : W ⟶ Z} {g' : W ⟶ X} {g : Z ⟶ Y},
  CategoryTheory.IsPullback f' g' g f → P g → P g'

Defined in: Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by: 3 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong

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Cites5

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.IsPullbackstatement · cited by 320
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongstatement and proof · cited by 24

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.pullback_sndproof · cited by 12
CategoryTheory.MorphismProperty.pullback_fstproof · cited by 4
CategoryTheory.MorphismProperty.isStableUnderBaseChangeAgainst_top_iffproof · cited by 0