Theorems · Theorem · category theory
CategoryTheory.IsCofilteredOrEmpty.cone_objs
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.IsCofilteredOrEmpty C] (X Y : C),
∃ W x x, Truefor every pair of objects there exists another object "to the left"
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.IsCofilteredOrEmptystatement and proof · cited by 55
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCofiltered.minproof · cited by 8
- CategoryTheory.IsCofiltered.cospanproof · cited by 6
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- CategoryTheory.exists_eq_of_isCofiltered_costructuredArrowproof · cited by 1
- CategoryTheory.Limits.IsCofiltered.sequentialFunctor_initial_auxproof · cited by 0
- CategoryTheory.Limits.IsCofiltered.sequentialFunctor_mapproof · cited by 0
- CategoryTheory.Functor.IsMittagLeffler.toPreimagesproof · cited by 0
- CategoryTheory.Functor.eval_section_injective_of_eventually_injectiveproof · cited by 0