Theorems · Theorem · category theory

CategoryTheory.Limits.preservesLimit_of_evaluation

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  {J : Type u₁} [inst_2 : CategoryTheory.Category.{v₁, u₁} J] {K : Type u₂}
  [inst_3 : CategoryTheory.Category.{v₂, u₂} K] (F : CategoryTheory.Functor D (CategoryTheory.Functor K C))
  (G : CategoryTheory.Functor J D),
  (∀ (k : K), CategoryTheory.Limits.PreservesLimit G (F.comp ((CategoryTheory.evaluation K C).obj k))) →
    CategoryTheory.Limits.PreservesLimit G F

F : D ⥤ K ⥤ C preserves the limit of some G : J ⥤ D if it does for each k : K.

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Basic

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category