Theorems · Theorem · category theory

CategoryTheory.hasLimitsEssentiallySmallSite

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) (A : Type u₃)
  [inst_1 : CategoryTheory.Category.{v₃, u₃} A] [inst_2 : CategoryTheory.EssentiallySmall.{w, v₁, u₁} C]
  [CategoryTheory.Limits.HasLimits
      (CategoryTheory.Sheaf ((CategoryTheory.equivSmallModel C).inverse.inducedTopology J) A)],
  CategoryTheory.Limits.HasLimitsOfSize.{max v₃ w, max v₃ w, max u₁ v₃, max (max (max u₃ u₁) v₃) v₁}
    (CategoryTheory.Sheaf J A)

Defined in

Mathlib.CategoryTheory.Sites.Equivalence

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.EssentiallySmallCategoryTheory.Limits.HasLimits