Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.plusObj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      {D : Type w} →
        [inst_1 : CategoryTheory.Category.{w', w} D] →
          [∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X),
                CategoryTheory.Limits.HasMultiequalizer (S.index P)] →
            CategoryTheory.Functor Cᵒᵖ D →
              [∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D] → CategoryTheory.Functor Cᵒᵖ D

The plus construction, associating a presheaf to any presheaf. See plusFunctor below for a functorial version.

Defined in

Mathlib.CategoryTheory.Sites.Plus

Cited by

56 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasMultiequalizerCategoryTheory.Limits.HasColimitsOfShape