Theorems · Definition · category theory

CategoryTheory.IsSplitEpi.casesOn

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      {f : X ⟶ Y} →
        {motive : CategoryTheory.IsSplitEpi f → Sort u} →
          (t : CategoryTheory.IsSplitEpi f) →
            ((exists_splitEpi : Nonempty (CategoryTheory.SplitEpi f)) → motive ⋯) → motive t

Defined in: Mathlib.CategoryTheory.EpiMono
Cited by: 5 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

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.Homstatement and proof · cited by 32,603
CategoryTheory.IsSplitEpistatement and proof · cited by 46
CategoryTheory.SplitEpistatement and proof · cited by 28

Cited by5

Results whose statement or proof uses this declaration.

SSet.unique_nonDegenerate_mapproof · cited by 3
CategoryTheory.ObjectProperty.IsStrongGenerator.mk_of_exists_colimitsOfShapeproof · cited by 2
SSet.unique_nonDegenerate_simplexproof · cited by 1
LightCondensed.internallyProjective_free_natUnionInftyproof · cited by 0
SSet.unique_nonDegenerate_dimproof · cited by 0