Theorems · Theorem · category theory
CategoryTheory.eqToHom_refl
∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] (X : C) (p : X = X),
CategoryTheory.eqToHom p = CategoryTheory.CategoryStruct.id X- Defined in
- Mathlib.CategoryTheory.EqToHom
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.eqToHomstatement · cited by 860
- CategoryTheory.CategoryStructstatement and proof · cited by 343
Cited by28
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.ext_of_isoproof · cited by 28
- CategoryTheory.Paths.ext_functorproof · cited by 6
- TopCat.Sheaf.eq_of_locally_eq'proof · cited by 6
- CategoryTheory.ComposableArrows.ext_succproof · cited by 5
- CategoryTheory.Pseudofunctor.mapComp'_comp_idproof · cited by 4
- CategoryTheory.Pseudofunctor.mapComp'_id_compproof · cited by 4
- CategoryTheory.comp_eqToHom_heqproof · cited by 2
- AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'proof · cited by 2
- CategoryTheory.eqToHom_comp_heqproof · cited by 2
- AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eqproof · cited by 1
- AlgebraicGeometry.Spec.sheafedSpaceMap_compproof · cited by 1