Theorems · Theorem · category theory

CategoryTheory.hasLimitsOfShape_of_hasLimitsOfShape_createsLimitsOfShape

∀ {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 C D)
  [CategoryTheory.Limits.HasLimitsOfShape J D] [CategoryTheory.CreatesLimitsOfShape J F],
  CategoryTheory.Limits.HasLimitsOfShape J C

If F creates limits of shape J, and D has limits of shape J, then C has limits of shape J.

Defined in

Mathlib.CategoryTheory.Limits.Creates

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.CreatesLimitsOfShape