Theorems · Theorem · category theory

CategoryTheory.Presieve.piComparison_fac

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (F : CategoryTheory.Functor Cᵒᵖ (Type w)) {α : Type u_1}
  [inst_1 : Small.{w, u_1} α] {X : α → C} (c : CategoryTheory.Limits.Cofan X) (hc : CategoryTheory.Limits.IsColimit c),
  have this := ⋯;
  (CategoryTheory.Limits.piComparison F fun x => Opposite.op (X x)) =
    CategoryTheory.CategoryStruct.comp
      (F.map
        (CategoryTheory.Limits.opCoproductIsoProduct' hc
            (CategoryTheory.Limits.productIsProduct fun x => Opposite.op (X x))).inv)
      (CategoryTheory.Equalizer.Presieve.Arrows.forkMap F X c.inj)

Defined in

Mathlib.CategoryTheory.Sites.Preserves

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategorySmall