Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.pushout_inl

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C} {A B A' : C}
  (f : A ⟶ A') (g : A ⟶ B) [inst_1 : CategoryTheory.Limits.HasPushout f g] [P.IsStableUnderCobaseChangeAlong f],
  P g → P (CategoryTheory.Limits.pushout.inl f g)

Defined in: Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by: 1 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasPushout CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong

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Cites9

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.Limits.pushoutstatement · cited by 284
CategoryTheory.Limits.HasPushoutstatement and proof · cited by 192
CategoryTheory.Limits.pushout.inlstatement · cited by 192
CategoryTheory.IsPushout.of_hasPushoutproof · cited by 20
CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongstatement and proof · cited by 16
CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong.of_isPushoutproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.IsStableUnderComposition.ind_of_preIndSpreadsproof · cited by 1