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Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C) {X Y : P.FullSubcategory}
  {f g : X ⟶ Y}, f.hom = g.hom → f = g
Defined in
Mathlib.CategoryTheory.ObjectProperty.FullSubcategory
Cited by
27 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
CategoryTheory.Category

Around this declaration

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

FGModuleCat.hom_ext · cited by 2FGModuleCat.hom_extSimplexCategory.Truncated.morphismProperty_eq_top · cited by 2Truncated.morphismPropert…CategoryTheory.Sheaf.toImage_ι · cited by 2Sheaf.toImage_ιSimplexCategory.Truncated.δ₂_two_comp_σ₂_one · cited by 2Truncated.δ₂_two_comp_σ₂_…SimplexCategory.Truncated.δ₂_two_comp_σ₂_zero · cited by 2Truncated.δ₂_two_comp_σ₂_…SimplexCategory.Truncated.δ₂_zero_comp_σ₂_one · cited by 2Truncated.δ₂_zero_comp_σ₂…SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zero · cited by 2Truncated.δ₂_zero_comp_σ₂…CategoryTheory.CardinalDirectedPoset.isCardinalPresentable_of_hasCardinalLT_of_le · cited by 2CardinalDirectedPoset.isC…CategoryTheory.Sheaf.hom_ext · cited by 2Sheaf.hom_extCategoryTheory.Sheaf.hom_ext_iff · cited by 2Sheaf.hom_ext_iffSimplexCategory.Truncated.Hom.ext · cited by 2Hom.extSimplexCategory.Truncated.δ₂_one_comp_σ₂_one · cited by 1Truncated.δ₂_one_comp_σ₂_…SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero · cited by 1Truncated.δ₂_one_comp_σ₂_…HomotopicalAlgebra.CofibrantObject.exists_bifibrant_map · cited by 1CofibrantObject.exists_bi…CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext · cited by 1FunctorsInverting.hom_extCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…CategoryTheory.InducedCategory.hom_ext · cited by 16InducedCategory.hom_extObjectProperty.hom_extCITED BYCITES

Cites7

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Cited by27

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