Theorems · Definition · category theory

CategoryTheory.Limits.Cocone.functorialityEquivalence

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {D : Type u₄} →
          [inst_2 : CategoryTheory.Category.{v₄, u₄} D] →
            (F : CategoryTheory.Functor J C) →
              (e : C ≌ D) → CategoryTheory.Limits.Cocone F ≌ CategoryTheory.Limits.Cocone (F.comp e.functor)

If e : C ≌ D is an equivalence of categories, then functoriality F e.functor induces an equivalence between cocones over F and cocones over F ⋙ e.functor.

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category