Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.plusMap_toPlus

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type w}
  [inst_1 : CategoryTheory.Category.{w', w} D]
  [inst_2 :
    ∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X), CategoryTheory.Limits.HasMultiequalizer (S.index P)]
  (P : CategoryTheory.Functor Cᵒᵖ D) [inst_3 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D],
  J.plusMap (J.toPlus P) = J.toPlus (J.plusObj P)

(P ⟶ P⁺)⁺ = P⁺ ⟶ P⁺⁺

Defined in

Mathlib.CategoryTheory.Sites.Plus

Cited by

5 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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