Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            (L : CategoryTheory.Functor C D) →
              (R : CategoryTheory.Functor E D) →
                CategoryTheory.Functor
                  (CategoryTheory.Grothendieck (R.comp (CategoryTheory.CostructuredArrow.functor L)))
                  (CategoryTheory.Comma L R)

The functor used to establish the equivalence grothendieckPrecompFunctorEquivalence between the Grothendieck construction on CostructuredArrow.functor and the comma category.

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Functor

Cited by

15 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category