Theorems · Definition · category theory
CategoryTheory.MorphismProperty.RespectsIso
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropP respects isomorphisms, if it respects the morphism property isomorphisms C, i.e.
it is stable under pre- and postcomposition with isomorphisms.
- Cited by
- 248 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
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
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.isomorphismsproof · cited by 66
- CategoryTheory.MorphismProperty.Respectsproof · cited by 2
Cited by284
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.arrow_mk_iso_iffstatement and proof · cited by 78
- CategoryTheory.MorphismProperty.cancel_left_of_respectsIsostatement and proof · cited by 33
- CategoryTheory.MorphismProperty.Comma.mapLeftIsostatement and proof · cited by 18
- CategoryTheory.MorphismProperty.Comma.mapRightIsostatement and proof · cited by 18
- CategoryTheory.MorphismProperty.cancel_right_of_respectsIsostatement and proof · cited by 16
- RingHom.toMorphismProperty_respectsIso_iffstatement and proof · cited by 11
- AlgebraicGeometry.Scheme.coverOfIsIsostatement and proof · cited by 9
- AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIsostatement and proof · cited by 8
- CategoryTheory.Localization.SmallShiftedHom.mk₀Invstatement and proof · cited by 8
- RingHom.RespectsIso.arrow_mk_iso_iffproof · cited by 6
- CategoryTheory.MorphismProperty.Over.pullbackCompstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.comma_iso_iffstatement and proof · cited by 5
Showing the 200 most cited of 284.