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Theorems · Inductive type · category theory

CategoryTheory.Presieve.singleton

{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (Y ⟶ X) → CategoryTheory.Presieve X

The singleton presieve.

Defined in
Mathlib.CategoryTheory.Sites.Sieves
Cited by
57 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Presieve.ofArrows_pUnit · cited by 10Presieve.ofArrows_pUnitCategoryTheory.Presieve.singleton.casesOn · cited by 9singleton.casesOnCategoryTheory.Presieve.FamilyOfElements.singletonEquiv · cited by 5FamilyOfElements.singleto…CategoryTheory.PreZeroHypercover.presieve₀_singleton · cited by 4PreZeroHypercover.presiev…CategoryTheory.Precoverage.mem_coverings_of_isIso · cited by 3Precoverage.mem_coverings…CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition · cited by 3Precoverage.mem_toGrothen…CategoryTheory.Presieve.singleton_self · cited by 3Presieve.singleton_selfCategoryTheory.Pretopology.ext · cited by 3Pretopology.extCategoryTheory.Presieve.isSheafFor_top · cited by 3Presieve.isSheafFor_topCategoryTheory.Presieve.ofArrows_of_unique · cited by 2Presieve.ofArrows_of_uniq…AlgebraicGeometry.Scheme.Hom.presieve₀_cover · cited by 2Hom.presieve₀_coverCategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply_self · cited by 2FamilyOfElements.singleto…AlgebraicGeometry.Scheme.Hom.singleton_mem_propQCPrecoverage · cited by 2Hom.singleton_mem_propQCP…CategoryTheory.Sieve.generateSingleton_eq · cited by 2Sieve.generateSingleton_eqCategoryTheory.Sieve.generate_of_singleton_isSplitEpi · cited by 2Sieve.generate_of_singlet…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Presieve · cited by 449CategoryTheory.PresievePresieve.singletonCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by71

Results whose statement or proof uses this declaration.