Theorems · Theorem · category theory

CategoryTheory.Adjunction.isCocontinuous_iff_coverPreserving

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (J : CategoryTheory.GrothendieckTopology C)
  (K : CategoryTheory.GrothendieckTopology D) {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G), F.IsCocontinuous J K ↔ CategoryTheory.CoverPreserving K J G

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category