Theorems · Theorem · category theory
CategoryTheory.Sieve.mem_functorPushforward_iff_of_full_of_faithful
∀ {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] [F.Faithful] {X Y : C} (R : CategoryTheory.Sieve X) (f : Y ⟶ X),
CategoryTheory.Presieve.functorPushforward F R.arrows (F.map f) ↔ R.arrows f- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.Functor.map_injectiveproof · cited by 91
- CategoryTheory.Presieve.functorPushforwardstatement · cited by 16
- CategoryTheory.Sieve.mem_functorPushforward_iff_of_fullproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.