Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.arrow_iso_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) [P.RespectsIso]
{f g : CategoryTheory.Arrow C} (e : f ≅ g), P f.hom ↔ P g.hom- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
- CategoryTheory.Arrow.homstatement · cited by 335
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- CategoryTheory.MorphismProperty.comma_iso_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.arrow_mk_iso_iffproof · cited by 78
- DerivedCategory.isIso_iffproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_iffproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iffproof · cited by 1