Theorems · Theorem · category theory

CategoryTheory.Limits.reflectsLimit_of_reflectsIsomorphisms

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] (F : CategoryTheory.Functor J C)
  (G : CategoryTheory.Functor C D) [G.ReflectsIsomorphisms] [CategoryTheory.Limits.HasLimit F]
  [CategoryTheory.Limits.PreservesLimit F G], CategoryTheory.Limits.ReflectsLimit F G

If the limit of F exists and G preserves it, then if G reflects isomorphisms then it reflects the limit of F (see also JointlyReflectIsomorphisms.jointlyReflectsColimit in the file CategoryTheory/Functor/ReflectsIso/Limits.lean for the corresponding result for a family of functors which joinly reflect isomorphisms).

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.ReflectsIsomorphismsCategoryTheory.Limits.HasLimitCategoryTheory.Limits.PreservesLimit