Theorems · Definition · category theory
CategoryTheory.pathsHomRel
(C : Type u₁) → [inst : CategoryTheory.Category.{v₁, u₁} C] → HomRel (CategoryTheory.Paths C)The canonical relation on the path category of a category: two paths are related if they compose to the same morphism.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Homproof · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Pathsstatement and proof · cited by 82
- HomRelstatement · cited by 49
- CategoryTheory.pathCompositionproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.quotientPathsTostatement and proof · cited by 2
- CategoryTheory.toQuotientPathsstatement and proof · cited by 2
- CategoryTheory.quotientPathsEquivstatement and proof · cited by 0
- CategoryTheory.quotientPathsTo_mapstatement and proof · cited by 0
- CategoryTheory.quotientPathsTo_objstatement and proof · cited by 0
- CategoryTheory.toQuotientPaths_mapstatement · cited by 0
- CategoryTheory.toQuotientPaths_obj_asstatement · cited by 0