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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
Defined in
Mathlib.CategoryTheory.MorphismProperty.Basic
Cited by
16 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.IsIso

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueField · cited by 2LocallyQuasiFinite.of_fib…AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso · cited by 2HasRingHomProperty.stalkM…AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion · cited by 1AlgebraicGeometry.isGermI…AlgebraicGeometry.HasRingHomProperty.of_stalkMap · cited by 1HasRingHomProperty.of_sta…AlgebraicGeometry.isIntegral_appTop_of_universallyClosed · cited by 1AlgebraicGeometry.isInteg…CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.mk' · cited by 1IsStableUnderCobaseChange…AlgebraicGeometry.hasOfPostcompProperty_isOpenImmersion_of_morphismRestrict · cited by 0AlgebraicGeometry.hasOfPo…AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_lift · cited by 0Scheme.isSeparated_iff_is…CategoryTheory.StructuredArrow.isClosedUnderLimitsOfShape · cited by 0StructuredArrow.isClosedU…AlgebraicGeometry.quasiSeparatedSpace_iff_quasiCompact_prod_lift · cited by 0AlgebraicGeometry.quasiSe…CategoryTheory.MorphismProperty.sourceLocalClosure.sourceLocalClosure_iff_of_respectsLeft · cited by 0sourceLocalClosure.source…CategoryTheory.MorphismProperty.CodescendsAlong.mk' · cited by 0CodescendsAlong.mk'AlgebraicGeometry.AffineTargetMorphismProperty.cancel_right_of_respectsIso · cited by 0AffineTargetMorphismPrope…RingHom.HasEqualizers.isClosedUnderLimitsOfShape · cited by 0HasEqualizers.isClosedUnd…RingHom.HasFiniteProducts.isClosedUnderLimitsOfShape · cited by 0HasFiniteProducts.isClose…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.MorphismProperty.RespectsIso · cited by 248MorphismProperty.Respects…CategoryTheory.IsIso.hom_inv_id · cited by 97IsIso.hom_inv_idCategoryTheory.MorphismProperty.RespectsIso.postcomp · cited by 3RespectsIso.postcompMorphismProperty.cancel_right…CITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.