Theorems · Theorem · category theory

CategoryTheory.Limits.hasColimit_of_equivalence_comp

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {K : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} K]
  {C : Type u} [inst_2 : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor J C} (e : K ≌ J)
  [CategoryTheory.Limits.HasColimit (e.functor.comp F)], CategoryTheory.Limits.HasColimit F

If a E ⋙ F has a colimit, and E is an equivalence, we can construct a colimit of F.

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit