Theorems · Definition · category theory

CategoryTheory.Grothendieck.pre

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} D] →
        (F : CategoryTheory.Functor C CategoryTheory.Cat) →
          (G : CategoryTheory.Functor D C) →
            CategoryTheory.Functor (CategoryTheory.Grothendieck (G.comp F)) (CategoryTheory.Grothendieck F)

Applying a functor G : D ⥤ C to the base of the Grothendieck construction induces a functor Grothendieck (G ⋙ F) ⥤ Grothendieck F.

Defined in

Mathlib.CategoryTheory.Grothendieck

Cited by

8 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category