Theorems · Inductive type · category theory
CategoryTheory.IsFilteredOrEmpty
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category IsFilteredOrEmpty if
1. for every pair of objects there exists another object "to the right", and
2. for every pair of parallel morphisms there exists a morphism to the right 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 by80
Results whose statement or proof uses this declaration.
- CategoryTheory.IsFiltered.leftToMaxstatement and proof · cited by 26
- CategoryTheory.IsFiltered.maxstatement and proof · cited by 26
- CategoryTheory.IsFiltered.rightToMaxstatement and proof · cited by 26
- CategoryTheory.IsFiltered.coeqstatement and proof · cited by 18
- CategoryTheory.IsFiltered.coeqHomstatement and proof · cited by 17
- CategoryTheory.IsFiltered.coeq_conditionstatement and proof · cited by 14
- CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff'statement and proof · cited by 10
- CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iffstatement and proof · cited by 9
- CategoryTheory.Functor.final_iff_of_isFilteredstatement and proof · cited by 6
- CategoryTheory.Limits.Types.FilteredColimit.isColimitOf'statement and proof · cited by 5
- CategoryTheory.IsFiltered.bowtiestatement and proof · cited by 5
- CategoryTheory.IsFiltered.spanstatement and proof · cited by 5