Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.IsLocalSite.from_terminal_mem_of_mem
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
[inst_1 : J.IsLocalSite] {X : C} (f : ⊤_ C ⟶ X) {S : CategoryTheory.Sieve X}, S ∈ J X → S.arrows fOn a local site, every covering sieve contains every morphism from the terminal object.
- Defined in
- Mathlib.CategoryTheory.Sites.LocalSite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsstatement · cited by 446
- CategoryTheory.Limits.terminalstatement and proof · cited by 141
- CategoryTheory.Sieve.pullbackproof · cited by 126
- CategoryTheory.GrothendieckTopology.pullback_stableproof · cited by 36
- CategoryTheory.GrothendieckTopology.IsLocalSitestatement and proof · cited by 10
- CategoryTheory.Sieve.mem_iff_pullback_eq_topproof · cited by 7
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