Theorems · Theorem · category theory

CategoryTheory.Presheaf.coconePtToShrinkYoneda_comp

∀ {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})}
  (hc' : CategoryTheory.Limits.IsColimit c') {P : CategoryTheory.Functor Cᵒᵖ (Type w)} (x : P.obj c.pt),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Presheaf.coconePtToShrinkYoneda c hc')
      (CategoryTheory.shrinkYonedaEquiv.symm x) =
    (CategoryTheory.Presheaf.coconeCompShrinkYonedaHomEquiv hc').symm
      (CategoryTheory.Limits.Types.sectionOfCone (P.mapCone c) x)

Defined in

Mathlib.CategoryTheory.Limits.Types.PreservesLimit

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.LocallySmall