Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.arrow_mk_mem_toSet_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) {X Y : C} (f : X ⟶ Y),
CategoryTheory.Arrow.mk f ∈ P.toSet ↔ P f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Arrow.mkstatement · cited by 421
- CategoryTheory.MorphismProperty.toSetstatement · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.ofHoms_iffproof · cited by 8
- CategoryTheory.SmallObject.SuccStruct.prop_iffproof · cited by 1
- CategoryTheory.MorphismProperty.isSmall_iff_eq_ofHomsproof · cited by 0
- CategoryTheory.MorphismProperty.of_eqproof · cited by 0