Theorems · Definition · category theory

CategoryTheory.StructuredArrow.preEquivalence

{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] →
            (F : CategoryTheory.Functor C D) →
              {G : CategoryTheory.Functor D E} →
                {e : E} →
                  (f : CategoryTheory.StructuredArrow e G) →
                    CategoryTheory.StructuredArrow f (CategoryTheory.StructuredArrow.pre e F G) ≌
                      CategoryTheory.StructuredArrow f.right F

A structured arrow category on a StructuredArrow.pre e F G functor is equivalent to the structured arrow category on F

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category