Theorems · Definition · category theory

CategoryTheory.Presheaf.preservesLimitHomFamily

{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] →
              (h : PLift (CategoryTheory.Limits.HasLimit F)) →
                CategoryTheory.Presheaf.preservesLimitHomFamilySrc F ⟶
                  CategoryTheory.Presheaf.preservesLimitHomFamilyTgt F h

Let F : J ⥤ Cᵒᵖ be a functor. This is the family of morphisms which consists of the single morphism colimit (F.leftOp ⋙ shrinkYoneda) ⟶ shrinkYoneda.obj (limit F).unop if F has a limit, or is the empty family otherwise.

Defined in

Mathlib.CategoryTheory.Limits.Types.PreservesLimit

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.LocallySmallSmall