Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.cancel_right_of_respectsIso
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) [hP : P.RespectsIso]
{X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) [CategoryTheory.IsIso g], P (CategoryTheory.CategoryStruct.comp f g) ↔ P f- Cited by
- 16 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invproof · cited by 467
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- CategoryTheory.IsIso.hom_inv_idproof · cited by 97
- CategoryTheory.MorphismProperty.RespectsIso.postcompproof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIsoproof · cited by 2
- AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersionproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.of_stalkMapproof · cited by 1
- AlgebraicGeometry.isIntegral_appTop_of_universallyClosedproof · cited by 1
- CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.mk'proof · cited by 1
- AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_liftproof · cited by 0
- CategoryTheory.StructuredArrow.isClosedUnderLimitsOfShapeproof · cited by 0
- AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_liftproof · cited by 0
- CategoryTheory.MorphismProperty.CodescendsAlong.mk'proof · cited by 0