Theorems · Theorem · category theory

CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_right

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {Y X Y' X' B A : C} (i : A ⟶ B) {p : X ⟶ Y}
  {p' : X' ⟶ Y'} (e : CategoryTheory.Arrow.mk p ≅ CategoryTheory.Arrow.mk p'),
  CategoryTheory.HasLiftingProperty i p ↔ CategoryTheory.HasLiftingProperty i p'

Defined in: Mathlib.CategoryTheory.LiftingProperties.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites8

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.Isostatement and proof · cited by 3,963
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.Arrowstatement · cited by 713
CategoryTheory.Arrow.mkstatement and proof · cited by 421
CategoryTheory.HasLiftingPropertystatement and proof · cited by 50
CategoryTheory.HasLiftingProperty.of_arrow_iso_rightproof · cited by 2

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isInitial_isTerminal_iff'proof · cited by 0
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isTerminal_iffproof · cited by 0
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isInitial_isTerminal_iffproof · cited by 0