Theorems · Definition · category theory
CategoryTheory.toQuotientPaths
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
CategoryTheory.Functor C (CategoryTheory.Quotient (CategoryTheory.pathsHomRel C))The functor from a category to the canonical quotient of its path category.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Functorstatement · cited by 16,252
- CategoryTheory.Pathsstatement · cited by 82
- CategoryTheory.Quotientstatement · cited by 48
- CategoryTheory.Quotient.asproof · cited by 47
- Quiver.Hom.toPathproof · cited by 38
- CategoryTheory.HomRel.CompClosureproof · cited by 19
- CategoryTheory.pathsHomRelstatement and proof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.quotientPathsEquivproof · cited by 0
- CategoryTheory.toQuotientPaths_mapstatement and proof · cited by 0
- CategoryTheory.toQuotientPaths_obj_asstatement and proof · cited by 0