Theorems · Theorem · category theory

CategoryTheory.Presieve.map_le_iff_le_functorPullback

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {X : C} {R : CategoryTheory.Presieve X} {S : CategoryTheory.Presieve (F.obj X)},
  CategoryTheory.Presieve.map F R ≤ S ↔ R ≤ CategoryTheory.Presieve.functorPullback F S

Defined in

Mathlib.CategoryTheory.Sites.Sieves

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category