Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.precomposeHomEquiv

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F G : CategoryTheory.Functor J C} →
          (α : F ≅ G) →
            (c : CategoryTheory.Limits.Cocone G) →
              CategoryTheory.Limits.IsColimit ((CategoryTheory.Limits.Cocone.precompose α.hom).obj c) ≃
                CategoryTheory.Limits.IsColimit c

A cocone precomposed with a natural isomorphism is a colimit cocone if and only if the original cocone is.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

17 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category