Theorems · Theorem · category theory

CategoryTheory.Presheaf.preservesLimit_eq_isLocal

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} J]
  [inst_2 : CategoryTheory.LocallySmall.{w, v, u} C] (F : CategoryTheory.Functor J Cᵒᵖ) [inst_3 : Small.{w, u'} J],
  CategoryTheory.ObjectProperty.preservesLimit F =
    (CategoryTheory.MorphismProperty.ofHoms (CategoryTheory.Presheaf.preservesLimitHomFamily F)).isLocal

Defined in

Mathlib.CategoryTheory.Limits.Types.PreservesLimit

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.LocallySmallSmall