Theorems · Theorem · category theory
CategoryTheory.IsFiltered.nonempty
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.IsFiltered C], Nonempty Ca filtered category must be non-empty
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.IsFiltered
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.IsFilteredstatement and proof · cited by 210
Cited by10
Results whose statement or proof uses this declaration.
- AddMonCat.FilteredColimits.colimit_zero_eqproof · cited by 2
- CategoryTheory.IsFinitelyPresentable.exists_hom_of_isColimit_underproof · cited by 2
- CategoryTheory.IsFiltered.sup_objs_existsproof · cited by 2
- CategoryTheory.Limits.isIndObject_of_isFiltered_of_finallySmallproof · cited by 1
- CategoryTheory.MorphismProperty.ind_iff_ind_underMkproof · cited by 1
- CategoryTheory.Functor.final_const_of_isTerminalproof · cited by 1
- MonCat.FilteredColimits.colimit_one_eqproof · cited by 1
- CategoryTheory.Functor.final_of_isFiltered_of_pUnitproof · cited by 0
- CategoryTheory.IsFiltered.exists_directedproof · cited by 0
- CategoryTheory.IsCardinalFiltered.nonemptyproof · cited by 0