Theorems · Theorem · category theory

CategoryTheory.Functor.IsCocontinuous.cover_lift

∀ {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} {G : CategoryTheory.Functor C D}
  {J : CategoryTheory.GrothendieckTopology C} {K : CategoryTheory.GrothendieckTopology D} [self : G.IsCocontinuous J K]
  {U : C} {S : CategoryTheory.Sieve (G.obj U)}, S ∈ K (G.obj U) → CategoryTheory.Sieve.functorPullback G S ∈ J U

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Functor.IsCocontinuous