Theorems · Definition · category theory
CategoryTheory.Quotient.functor
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] → (r : HomRel C) → CategoryTheory.Functor C (CategoryTheory.Quotient r)The functor from a category to its quotient.
- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HomRelstatement and proof · cited by 49
- CategoryTheory.Quotientstatement · cited by 48
- CategoryTheory.Quotient.asproof · cited by 47
- CategoryTheory.HomRel.CompClosureproof · cited by 19
Cited by66
Results whose statement or proof uses this declaration.
- HomotopyCategory.quotientproof · cited by 109
- CategoryTheory.MorphismProperty.Qproof · cited by 98
- SimplexCategoryGenRel.σproof · cited by 26
- CategoryTheory.FreeGroupoid.ofproof · cited by 21
- SimplexCategoryGenRel.δproof · cited by 20
- HomotopicalAlgebra.BifibrantObject.toHoCatproof · cited by 20
- CategoryTheory.Cat.FreeRefl.mkproof · cited by 17
- CategoryTheory.Quotient.soundstatement · cited by 16
- HomotopicalAlgebra.CofibrantObject.toHoCatproof · cited by 14
- HomotopicalAlgebra.FibrantObject.toHoCatproof · cited by 8
- CategoryTheory.Cat.FreeRefl.quotientFunctorproof · cited by 8
- CategoryTheory.Quotient.natTransLiftstatement and proof · cited by 7