Theorems · Definition · category theory

CategoryTheory.Equalizer.Presieve.Arrows.SecondObj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    CategoryTheory.Functor Cᵒᵖ (Type w) →
      {B : C} →
        {I : Type t} →
          [Small.{w, t} I] →
            (X : I → C) →
              (π : (i : I) → X i ⟶ B) → [(CategoryTheory.Presieve.ofArrows X π).HasPairwisePullbacks] → Type w

The rightmost object of the fork diagram of the Stacks entry. The difference between this and Equalizer.Presieve.SecondObj P (ofArrows X π) arises if the family of arrows π contains duplicates. The Presieve.ofArrows doesn't see those.

Defined in

Mathlib.CategoryTheory.Sites.EqualizerSheafCondition

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategorySmallCategoryTheory.Presieve.HasPairwisePullbacks