Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.eqToHom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G : CategoryTheory.Functor C D} (h : F = G) (X : C), (CategoryTheory.eqToHom h).app X = CategoryTheory.eqToHom ⋯
Defined in
Mathlib.CategoryTheory.EqToHom
Cited by
22 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.ComposableArrows.ext_succ · cited by 5ComposableArrows.ext_succCategoryTheory.shiftFunctorAdd'_add_zero · cited by 3CategoryTheory.shiftFunct…CategoryTheory.shiftFunctorAdd'_assoc · cited by 3CategoryTheory.shiftFunct…CategoryTheory.Grothendieck.map_map · cited by 2Grothendieck.map_mapCochainComplex.ι_mapBifunctorShift₁Iso_hom_f · cited by 2CochainComplex.ι_mapBifun…CategoryTheory.Functor.curry_obj_uncurry_obj · cited by 2Functor.curry_obj_uncurry…CategoryTheory.shiftFunctorAdd'_zero_add · cited by 2CategoryTheory.shiftFunct…CategoryTheory.Grothendieck.map_map_fiber · cited by 1Grothendieck.map_map_fiberAlgebraicGeometry.Spec.basicOpen_hom_ext · cited by 1Spec.basicOpen_hom_extCategoryTheory.pullbackShiftFunctorZero'_inv_app · cited by 1CategoryTheory.pullbackSh…CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding · cited by 1Idempotents.toKaroubi_com…CategoryTheory.Grothendieck.map_comp_eq · cited by 0Grothendieck.map_comp_eqAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_fst · cited by 0IsOpenImmersion.pullbackC…CategoryTheory.Cat.eqToHom_app · cited by 0Cat.eqToHom_appAlgebraicGeometry.PresheafedSpace.ofRestrict_top_c · cited by 0PresheafedSpace.ofRestric…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.eqToHom · cited by 860CategoryTheory.eqToHomCategoryTheory.Functor.congr_obj · cited by 27Functor.congr_objCategoryTheory.eqToHom_appCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by22

Results whose statement or proof uses this declaration.