Theorems · Theorem · category theory
CategoryTheory.SmallObject.SuccStruct.prop.fac
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.SmallObject.SuccStruct C} {X Y : C}
{f : X ⟶ Y} (hf : Φ.prop f), f = CategoryTheory.CategoryStruct.comp (Φ.toSucc X) (CategoryTheory.eqToHom ⋯)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.eqToHomstatement · cited by 860
- CategoryTheory.SmallObject.SuccStructstatement and proof · cited by 54
- CategoryTheory.MorphismProperty.ofHoms.casesOnproof · cited by 26
- CategoryTheory.SmallObject.SuccStruct.propstatement and proof · cited by 18
- CategoryTheory.SmallObject.SuccStruct.succstatement and proof · cited by 15
- CategoryTheory.SmallObject.SuccStruct.toSuccstatement and proof · cited by 10
- CategoryTheory.SmallObject.SuccStruct.prop.succ_eqstatement · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succproof · cited by 2
- CategoryTheory.SmallObject.SuccStruct.prop.fac_assocproof · cited by 0