Theorems · Theorem · category theory
CategoryTheory.IsCofiltered.nonempty
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.IsCofiltered C], Nonempty Ca cofiltered category must be non-empty
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.IsCofiltered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.IsCofilteredstatement and proof · cited by 133
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCofiltered.inf_objs_existsproof · cited by 7
- CategoryTheory.Comma.isCofiltered_of_isCofiltered_costructuredArrowproof · cited by 3
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.Scheme.compactSpace_of_isLimitproof · cited by 2
- CategoryTheory.Functor.initial_const_of_isInitialproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- AlgebraicGeometry.isBasis_preimage_isAffineOpenproof · cited by 1
- CategoryTheory.Comma.initial_fst_of_isCofiltered_costructuredArrowproof · cited by 1
- CategoryTheory.Functor.initial_of_isCofiltered_pUnitproof · cited by 0