Theorems · Definition · category theory

CategoryTheory.Quotient.casesOn

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {r : HomRel C} →
      {motive : CategoryTheory.Quotient r → Sort u} →
        (t : CategoryTheory.Quotient r) → ((as : C) → motive { as := as }) → motive t

Defined in: Mathlib.CategoryTheory.Quotient
Cited by: 8 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

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Cites3

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
HomRelstatement and proof · cited by 49
CategoryTheory.Quotientstatement and proof · cited by 48

Cited by12

Results whose statement or proof uses this declaration.

SimplexCategoryGenRel.lenproof · cited by 6
CategoryTheory.Localization.Construction.morphismProperty_eq_topproof · cited by 2
SSet.Truncated.HomotopyCategory.mk_surjectiveproof · cited by 2
CategoryTheory.Localization.Construction.uniqproof · cited by 2
CategoryTheory.Quotient.inductionproof · cited by 1
CategoryTheory.quotientPathsEquivproof · cited by 0
CategoryTheory.Quotient.natTrans_extproof · cited by 0
CategoryTheory.Quotient.noConfusionproof · cited by 0
CategoryTheory.Quotient.noConfusionTypeproof · cited by 0
HomotopyCategory.quasiIso_eq_quasiIso_map_quotientproof · cited by 0
HomotopyCategory.Pretriangulated.contractible_distinguishedproof · cited by 0
HomologicalComplexUpToQuasiIso.Qh_inverts_quasiIsoproof · cited by 0