Theorems · Theorem · category theory
CategoryTheory.SmallObject.SuccStruct.prop_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.SmallObject.SuccStruct C) {X Y : C}
(f : X ⟶ Y), Φ.prop f ↔ CategoryTheory.Arrow.mk f = Φ.toSuccArrow X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Arrowstatement and proof · cited by 713
- CategoryTheory.Arrow.leftproof · cited by 426
- CategoryTheory.Arrow.mkstatement and proof · cited by 421
- CategoryTheory.SmallObject.SuccStructstatement and proof · cited by 54
- CategoryTheory.MorphismProperty.toSetproof · cited by 26
- CategoryTheory.MorphismProperty.ofHoms.casesOnproof · cited by 26
- CategoryTheory.SmallObject.SuccStruct.propstatement and proof · cited by 18
- CategoryTheory.SmallObject.SuccStruct.succproof · cited by 15
- CategoryTheory.SmallObject.SuccStruct.toSuccArrowstatement and proof · cited by 14
- CategoryTheory.SmallObject.SuccStruct.toSuccproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.SuccStruct.Iteration.prop_map_succproof · cited by 0