Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.pushout_inl_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P Q : CategoryTheory.MorphismProperty C} {Z X Y : C}
  {f : Z ⟶ X} {g : Z ⟶ Y} [P.IsStableUnderCobaseChange] [P.CodescendsAlong Q]
  [inst_3 : CategoryTheory.Limits.HasPushout f g], Q f → (P (CategoryTheory.Limits.pushout.inl f g) ↔ P g)

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

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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.MorphismProperty.IsStableUnderCobaseChangestatement and proof · cited by 33
CategoryTheory.IsPushout.of_hasPushoutproof · cited by 20
CategoryTheory.MorphismProperty.CodescendsAlongstatement and proof · cited by 9
CategoryTheory.MorphismProperty.iff_of_isPushoutproof · cited by 2

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