Theorems · Theorem · category theory

CategoryTheory.CommSq.right_adjoint_hasLift_iff

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {G : CategoryTheory.Functor C D} {F : CategoryTheory.Functor D C}
  {A B : C} {X Y : D} {i : A ⟶ B} {p : X ⟶ Y} {u : G.obj A ⟶ X} {v : G.obj B ⟶ Y}
  (sq : CategoryTheory.CommSq u (G.map i) p v) (adj : G ⊣ F), ⋯.HasLift ↔ sq.HasLift

A (right) adjoint square has a lifting if and only if the original square has a lifting.

Defined in

Mathlib.CategoryTheory.LiftingProperties.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category