Theorems · Theorem · category theory
CategoryTheory.IsCofiltered.inf_objs_exists
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsCofiltered C] (O : Finset C),
∃ S, ∀ {X : C}, X ∈ O → Nonempty (S ⟶ X)Any finite collection of objects in a cofiltered category has an object "to the left".
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Finsetstatement and proof · cited by 13,712
- eq_or_neproof · cited by 1,117
- Nonempty.someproof · cited by 340
- CategoryTheory.IsCofilteredstatement and proof · cited by 133
- Finset.inductionproof · cited by 108
- CategoryTheory.IsCofiltered.nonemptyproof · cited by 9
- CategoryTheory.IsCofiltered.minproof · cited by 8
- Finset.mem_of_mem_insert_of_neproof · cited by 8
- CategoryTheory.IsCofiltered.minToLeftproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCofiltered.inf_existsproof · cited by 6
- AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine_of_finiteproof · cited by 2
- Profinite.exists_isClopen_of_cofilteredproof · cited by 1
- TopCat.isTopologicalBasis_cofiltered_limitproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- Profinite.exists_locallyConstant_finite_auxproof · cited by 1
- AlgebraicGeometry.exists_preimage_eqproof · cited by 1