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- 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.
Cites7
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.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.InducedCategory.Hom.homstatement and proof · cited by 850
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.FullSubcategorystatement and proof · cited by 726
- CategoryTheory.InducedCategory.hom_extproof · cited by 16
Cited by27
Results whose statement or proof uses this declaration.
- FGModuleCat.hom_extproof · cited by 2
- SimplexCategory.Truncated.morphismProperty_eq_topproof · cited by 2
- CategoryTheory.Sheaf.toImage_ιproof · cited by 2
- SimplexCategory.Truncated.δ₂_two_comp_σ₂_oneproof · cited by 2
- SimplexCategory.Truncated.δ₂_two_comp_σ₂_zeroproof · cited by 2
- SimplexCategory.Truncated.δ₂_zero_comp_σ₂_oneproof · cited by 2
- SimplexCategory.Truncated.δ₂_zero_comp_σ₂_zeroproof · cited by 2
- CategoryTheory.Sheaf.hom_extproof · cited by 2
- CategoryTheory.Sheaf.hom_ext_iffproof · cited by 2
- SimplexCategory.Truncated.Hom.extproof · cited by 2
- SimplexCategory.Truncated.δ₂_one_comp_σ₂_oneproof · cited by 1