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Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.ext

∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] (W W' : CategoryTheory.MorphismProperty C),
  (∀ ⦃X Y : C⦄ (f : X ⟶ Y), W f ↔ W' f) → W = W'
Defined in
Mathlib.CategoryTheory.MorphismProperty.Basic
Cited by
61 results in Mathlib
Foundations
Depth 5 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.CategoryStruct

Around this declaration

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

CategoryTheory.ObjectProperty.isLocal_eq_inverseImage_isomorphisms · cited by 3ObjectProperty.isLocal_eq…CategoryTheory.MorphismProperty.ofHoms_homFamily · cited by 2MorphismProperty.ofHoms_h…SimplexCategory.Truncated.morphismProperty_eq_top · cited by 2Truncated.morphismPropert…CategoryTheory.GrothendieckTopology.W_inverseImage_whiskeringLeft · cited by 2GrothendieckTopology.W_in…AlgebraicGeometry.HasRingHomProperty.of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget · cited by 2HasRingHomProperty.of_isZ…CategoryTheory.Abelian.isoModSerre_kernel_eq_inverseImage_isomorphisms · cited by 2Abelian.isoModSerre_kerne…CategoryTheory.MorphismProperty.op_isomorphisms · cited by 2MorphismProperty.op_isomo…CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_eq_of_orderIso · cited by 2MorphismProperty.transfin…HomotopyCategory.inverseImage_quotient_isomorphisms · cited by 2HomotopyCategory.inverseI…HomotopyCategory.quasiIso_eq_trW_subcategoryAcyclic · cited by 2HomotopyCategory.quasiIso…CategoryTheory.MorphismProperty.map_eq_isoClosure · cited by 2MorphismProperty.map_eq_i…AlgebraicGeometry.geometrically_eq_universally · cited by 2AlgebraicGeometry.geometr…CategoryTheory.Paths.morphismProperty_eq_top · cited by 1Paths.morphismProperty_eq…AlgebraicGeometry.HasRingHomProperty.ext · cited by 1HasRingHomProperty.extCategoryTheory.ObjectProperty.trW_op · cited by 1ObjectProperty.trW_opQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…MorphismProperty.extCITED BYCITES

Cites3

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Cited by61

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