Theorems · Theorem · category theory

CategoryTheory.NatTrans.Equifibered.whiskerRight

∀ {J : Type u_1} {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_3} C] [inst_2 : CategoryTheory.Category.{v_4, u_4} D]
  {F G : CategoryTheory.Functor J C} {α : F ⟶ G},
  CategoryTheory.NatTrans.Equifibered α →
    ∀ (H : CategoryTheory.Functor C D)
      [∀ (i j : J) (f : j ⟶ i),
          CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan (α.app i) (G.map f)) H],
      CategoryTheory.NatTrans.Equifibered (CategoryTheory.Functor.whiskerRight α H)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered

Cited by

5 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimit