Mathlib Map

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
Assumes
CategoryTheory.CategoryStruct

Around this declaration

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

CategoryTheory.Functor.ext_of_iso · cited by 28Functor.ext_of_isoCategoryTheory.Paths.ext_functor · cited by 6Paths.ext_functorTopCat.Sheaf.eq_of_locally_eq' · cited by 6Sheaf.eq_of_locally_eq'CategoryTheory.ComposableArrows.ext_succ · cited by 5ComposableArrows.ext_succCategoryTheory.Pseudofunctor.mapComp'_comp_id · cited by 4Pseudofunctor.mapComp'_co…CategoryTheory.Pseudofunctor.mapComp'_id_comp · cited by 4Pseudofunctor.mapComp'_id…CategoryTheory.comp_eqToHom_heq · cited by 2CategoryTheory.comp_eqToH…AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen' · cited by 2Opens.ι_image_basicOpen'CategoryTheory.eqToHom_comp_heq · cited by 2CategoryTheory.eqToHom_co…AlgebraicGeometry.IsOpenImmersion.app_eq_appIso_inv_app_of_comp_eq · cited by 1IsOpenImmersion.app_eq_ap…CategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inl · cited by 1isPushout.multicofork_π_e…AlgebraicGeometry.Spec.sheafedSpaceMap_comp · cited by 1Spec.sheafedSpaceMap_compCategoryTheory.Limits.Multicofork.IsColimit.isPushout.multicofork_π_eq_inr · cited by 1isPushout.multicofork_π_e…AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom · cited by 1stalkMap.congr_homChainComplex.mk_d · cited by 1ChainComplex.mk_dQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.eqToHom · cited by 860CategoryTheory.eqToHomCategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.eqToHom_reflCITED BYCITES

Cites4

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Cited by28

Results whose statement or proof uses this declaration.