Theorems · Theorem · category theory
CategoryTheory.types_congr_hom
∀ {X Y : Type u} {f g : X ⟶ Y},
f = g → ∀ (x : X), (CategoryTheory.ConcreteCategory.hom f) x = (CategoryTheory.ConcreteCategory.hom g) x- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 149 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 73 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.ConcreteCategory.congr_homproof · cited by 138
Cited by149
Results whose statement or proof uses this declaration.
- CategoryTheory.isSheaf_iff_isSheaf_of_typeproof · cited by 30
- CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff'proof · cited by 10
- CategoryTheory.OverPresheafAux.YonedaCollection.extproof · cited by 9
- CategoryTheory.Presieve.compatible_iff_sieveCompatibleproof · cited by 6
- Traversable.toList_specproof · cited by 6
- CategoryTheory.ofHom_epi_iff_surjectiveproof · cited by 5
- CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_compatibleproof · cited by 5
- CategoryTheory.OverPresheafAux.YonedaCollection.map₂_sndproof · cited by 5
- SSet.Subcomplex.mem_degenerate_iffproof · cited by 5
- CategoryTheory.Functor.IsCoverDense.Types.naturality_applyproof · cited by 4
- SSet.degenerate_eq_iUnion_range_σproof · cited by 4
- CategoryTheory.Functor.isContinuous_of_coverPreservingproof · cited by 4