Theorems · Definition · category theory

CategoryTheory.Presheaf.coconePtToShrinkYoneda

{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} →
            (c : CategoryTheory.Limits.Cone F) →
              {c' : CategoryTheory.Limits.Cocone (F.leftOp.comp CategoryTheory.shrinkYoneda.{w, v, u})} →
                CategoryTheory.Limits.IsColimit c' →
                  (c'.pt ⟶ CategoryTheory.shrinkYoneda.{w, v, u}.obj (Opposite.unop c.pt))

Let F : J ⥤ Cᵒᵖ be a functor, c' a colimit cocone for F.leftOp ⋙ shrinkYoneda.{w}. For any cone c for F, this is the canonical natural transformation c'.pt ⟶ shrinkYoneda.{w}.obj c.pt.unop.

Defined in

Mathlib.CategoryTheory.Limits.Types.PreservesLimit

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.LocallySmall