Theorems · Inductive type · category theory
CategoryTheory.IsCofilteredOrEmpty
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category IsCofilteredOrEmpty if
1. for every pair of objects there exists another object "to the left", and
2. for every pair of parallel morphisms there exists a morphism to the left so the compositions
are equal.
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by76
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCofiltered.eqstatement and proof · cited by 8
- CategoryTheory.IsCofiltered.minstatement and proof · cited by 8
- CategoryTheory.IsCofilteredOrEmpty.cone_objsstatement and proof · cited by 8
- CategoryTheory.IsCofiltered.minToLeftstatement and proof · cited by 7
- CategoryTheory.IsCofiltered.minToRightstatement and proof · cited by 7
- CategoryTheory.IsCofiltered.cospanstatement and proof · cited by 6
- CategoryTheory.IsCofiltered.eqHomstatement and proof · cited by 6
- CategoryTheory.IsCofilteredOrEmpty.cone_mapsstatement and proof · cited by 5
- CategoryTheory.Functor.initial_iff_of_isCofilteredstatement and proof · cited by 5
- nonempty_sections_of_finite_cofiltered_systemstatement and proof · cited by 4
- CategoryTheory.IsCofiltered.eq_conditionstatement and proof · cited by 4
- CategoryTheory.Functor.toEventualRangesstatement and proof · cited by 4