Theorems · Definition · category theory

CategoryTheory.Over.mapPullbackAdj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      (f : X ⟶ Y) →
        [inst_1 : CategoryTheory.Limits.HasPullbacksAlong f] →
          CategoryTheory.Over.map f ⊣ CategoryTheory.Over.pullback f

Over.map f is left adjoint to Over.pullback f.

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

8 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlong