Theorems · Theorem · category theory

CategoryTheory.Sieve.mem_functorPushforward_iff_of_full

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [F.Full] {X Y : C} (R : CategoryTheory.Sieve X) (f : F.obj Y ⟶ F.obj X),
  CategoryTheory.Presieve.functorPushforward F R.arrows f ↔ ∃ g, F.map g = f ∧ R.arrows g

Defined in

Mathlib.CategoryTheory.Sites.Sieves

Cited by

1 results in Mathlib

Foundations

Depth 6 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Full