Theorems · Theorem · category theory

CategoryTheory.hasLimitsOfShape_of_reflective

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type u} [inst_2 : CategoryTheory.Category.{v, u} J] [CategoryTheory.Limits.HasLimitsOfShape J C]
  (R : CategoryTheory.Functor D C) [CategoryTheory.Reflective R], CategoryTheory.Limits.HasLimitsOfShape J D

If C has limits of shape J then any reflective subcategory has limits of shape J.

Defined in

Mathlib.CategoryTheory.Monad.Limits

Cited by

2 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Reflective