Theorems · Inductive type · category theory
CategoryTheory.Quotient
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → HomRel C → Type u_1A type synonym for C, thought of as the objects of the quotient category.
- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- HomRelstatement · cited by 49
Cited by91
Results whose statement or proof uses this declaration.
- HomotopyCategoryproof · cited by 132
- CategoryTheory.MorphismProperty.Localizationproof · cited by 72
- SSet.Truncated.HomotopyCategoryproof · cited by 54
- CategoryTheory.Quotient.asstatement and proof · cited by 47
- CategoryTheory.Quotient.functorstatement · cited by 41
- SimplexCategoryGenRelproof · cited by 39
- CategoryTheory.Cat.FreeReflproof · cited by 34
- CategoryTheory.FreeGroupoidproof · cited by 27
- CategoryTheory.FreeGroupoid.ofproof · cited by 21
- HomotopicalAlgebra.BifibrantObject.HoCatproof · cited by 20
- HomotopicalAlgebra.CofibrantObject.HoCatproof · cited by 17
- CategoryTheory.Quotient.soundstatement · cited by 16