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Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.cancel_left_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 f], P (CategoryTheory.CategoryStruct.comp f g) ↔ P g
Defined in
Mathlib.CategoryTheory.MorphismProperty.Basic
Cited by
33 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.AffineTargetMorphismProperty.cancel_left_of_respectsIso · cited by 8AffineTargetMorphismPrope…AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChange · cited by 3HasAffineProperty.isStabl…AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHom · cited by 2IsIntegralHom.iff_univers…AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso · cited by 2HasRingHomProperty.stalkM…AlgebraicGeometry.of_pullback_fst_Spec_of_codescendsAlong · cited by 2AlgebraicGeometry.of_pull…CategoryTheory.MorphismProperty.IsStableUnderBaseChange.mk' · cited by 2IsStableUnderBaseChange.m…AlgebraicGeometry.IsZariskiLocalAtSource.mk' · cited by 2IsZariskiLocalAtSource.mk'AlgebraicGeometry.IsZariskiLocalAtSource.of_openCover · cited by 2IsZariskiLocalAtSource.of…AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompact · cited by 2IsZariskiLocalAtTarget.de…AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpace · cited by 1AlgebraicGeometry.isFinit…AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion · cited by 1AlgebraicGeometry.isGermI…AlgebraicGeometry.HasRingHomProperty.of_stalkMap · cited by 1HasRingHomProperty.of_sta…CategoryTheory.MorphismProperty.IsLocalAtTarget.of_isPullback · cited by 1IsLocalAtTarget.of_isPull…CategoryTheory.MorphismProperty.pullbackMap · cited by 1MorphismProperty.pullback…CategoryTheory.MorphismProperty.universally_mk' · cited by 1MorphismProperty.universa…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.MorphismProperty.RespectsIso · cited by 248MorphismProperty.Respects…CategoryTheory.IsIso.inv_hom_id_assoc · cited by 37IsIso.inv_hom_id_assocCategoryTheory.MorphismProperty.RespectsIso.precomp · cited by 3RespectsIso.precompMorphismProperty.cancel_left_…CITED BYCITES

Cites9

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

Cited by33

Results whose statement or proof uses this declaration.