Theorems · Theorem · category theory
CategoryTheory.Sieve.id_mem_iff_eq_top
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {S : CategoryTheory.Sieve X},
S.arrows (CategoryTheory.CategoryStruct.id X) ↔ S = ⊤If the identity arrow is in a sieve, the sieve is maximal.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 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.
Cites9
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.Homproof · cited by 32,603
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- top_uniqueproof · cited by 102
- CategoryTheory.Sieve.downward_closedproof · cited by 39
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.mem_iff_pullback_eq_topproof · cited by 7
- CategoryTheory.Sieve.generate_of_contains_isSplitEpiproof · cited by 3
- TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscreteproof · cited by 2