Theorems · Theorem · category theory

CategoryTheory.Functor.functorPushforward_mem_iff

∀ {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) (G : CategoryTheory.Functor C D) {X : C} {S : CategoryTheory.Sieve X}
  [CategoryTheory.Functor.IsDenseSubsite J K G], CategoryTheory.Sieve.functorPushforward G S ∈ K (G.obj X) ↔ S ∈ J X

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite