Theorems · Definition · category theory
CategoryTheory.IsSiftedOrEmpty
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category C IsSiftedOrEmpty if the diagonal functor C ⥤ C × C is final.
- Defined in
- Mathlib.CategoryTheory.Limits.Sifted
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Functor.Finalproof · cited by 112
- CategoryTheory.Functor.diagproof · cited by 36
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.IsSifted.isSiftedOrEmpty_of_colim_preservesFiniteProductsstatement · cited by 1
- CategoryTheory.IsSifted.isSiftedOrEmpty_of_colim_preservesBinaryProductsstatement · cited by 1
- CategoryTheory.IsSifted.of_colim_preservesFiniteProductsproof · cited by 1
- CategoryTheory.IsFilteredOrEmpty.isSiftedOrEmptystatement · cited by 0