Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.baseChange_obj

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C} {S S' : C} (f : S' ⟶ S)
  [inst_1 : CategoryTheory.Limits.HasPullbacksAlong f] [P.IsStableUnderBaseChangeAlong f] (X : CategoryTheory.Over S),
  P X.hom → P ((CategoryTheory.Over.pullback f).obj X).hom

Defined in: Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by: 0 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasPullbacksAlong CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Overstatement and proof · cited by 935
CategoryTheory.Over.leftstatement and proof · cited by 541
CategoryTheory.Over.homstatement and proof · cited by 370
CategoryTheory.Over.pullbackstatement · cited by 53
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongstatement and proof · cited by 24
CategoryTheory.Limits.HasPullbacksAlongstatement and proof · cited by 21
CategoryTheory.MorphismProperty.pullback_sndproof · cited by 12

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