Theorems · Theorem · category theory
CategoryTheory.Presieve.exists_eq_ofArrows
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (R : CategoryTheory.Presieve X),
∃ ι Y f, R = CategoryTheory.Presieve.ofArrows Y f- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- le_antisymmproof · cited by 2,068
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Presieve.ofArrowsstatement and proof · cited by 150
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.mem_iff_exists_zeroHypercoverproof · cited by 8
- CategoryTheory.Pseudofunctor.IsStackFor.of_leproof · cited by 2
- CategoryTheory.Pseudofunctor.isPrestackFor_iff_of_sieve_eqproof · cited by 1
- CategoryTheory.Precoverage.comap_compproof · cited by 1
- CategoryTheory.Pseudofunctor.isStackFor_iff_of_sieve_eqproof · cited by 1
- CategoryTheory.Precoverage.pullbackArrows_memproof · cited by 1
- CategoryTheory.MorphismProperty.comap_precoverageproof · cited by 0