Mathlib Map

Theorems · Definition · category theory

CategoryTheory.DifferentialObject.Hom.f

{S : Type u_1} →
  [inst : AddMonoidWithOne S] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.HasShift C S] →
            {X Y : CategoryTheory.DifferentialObject S C} → X.Hom Y → (X.obj ⟶ Y.obj)

The morphism between underlying objects of the two differentiable objects.

Defined in
Mathlib.CategoryTheory.DifferentialObject
Cited by
28 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
AddMonoidWithOneCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShift

Around this declaration

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

HomologicalComplex.dgoToHomologicalComplex · cited by 10HomologicalComplex.dgoToH…CategoryTheory.DifferentialObject.shiftFunctor · cited by 7DifferentialObject.shiftF…CategoryTheory.DifferentialObject.isoApp · cited by 5DifferentialObject.isoAppCategoryTheory.Functor.mapDifferentialObject · cited by 3Functor.mapDifferentialOb…CategoryTheory.DifferentialObject.Hom.ext · cited by 2Hom.extCategoryTheory.DifferentialObject.eqToHom_f' · cited by 1DifferentialObject.eqToHo…CategoryTheory.DifferentialObject.ext · cited by 1DifferentialObject.extCategoryTheory.DifferentialObject.Hom.comm · cited by 1Hom.commCategoryTheory.DifferentialObject.Hom.comp · cited by 1Hom.compCategoryTheory.DifferentialObject.comp_f · cited by 0DifferentialObject.comp_fHomologicalComplex.homologicalComplexToDGO_map_f · cited by 0HomologicalComplex.homolo…CategoryTheory.Functor.mapDifferentialObject_map_f · cited by 0Functor.mapDifferentialOb…CategoryTheory.DifferentialObject.eqToHom_f · cited by 0DifferentialObject.eqToHo…CategoryTheory.DifferentialObject.eqToHom_f'_assoc · cited by 0DifferentialObject.eqToHo…CategoryTheory.DifferentialObject.ext_iff · cited by 0DifferentialObject.ext_iffCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftAddMonoidWithOne · cited by 313AddMonoidWithOneCategoryTheory.DifferentialObject · cited by 61CategoryTheory.Differenti…CategoryTheory.DifferentialObject.obj · cited by 50DifferentialObject.objCategoryTheory.DifferentialObject.Hom · cited by 9DifferentialObject.HomHom.fCITED BYCITES

Cites8

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Cited by34

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