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Theorems · Definition · category theory

CategoryTheory.DifferentialObject.d

{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] →
            (self : CategoryTheory.DifferentialObject S C) → self.obj ⟶ (CategoryTheory.shiftFunctor C 1).obj self.obj

The differential of a differential object.

Defined in
Mathlib.CategoryTheory.DifferentialObject
Cited by
23 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidWithOneCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShift
Mathlib docsSourceLoogleLeanSearch

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.Functor.mapDifferentialObject · cited by 3Functor.mapDifferentialOb…CategoryTheory.DifferentialObject.mkIso · cited by 3DifferentialObject.mkIsoCategoryTheory.DifferentialObject.d_squared · cited by 2DifferentialObject.d_squa…CategoryTheory.DifferentialObject.Hom.ext · cited by 2Hom.extCategoryTheory.DifferentialObject.d_squared_apply · cited by 1DifferentialObject.d_squa…CategoryTheory.DifferentialObject.objEqToHom_d · cited by 1DifferentialObject.objEqT…CategoryTheory.DifferentialObject.Hom.mk.inj · cited by 1mk.injCategoryTheory.DifferentialObject.Hom.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.DifferentialObject.Hom.comm · cited by 1Hom.commCategoryTheory.DifferentialObject.HomSubtype · cited by 0DifferentialObject.HomSub…CategoryTheory.Functor.mapDifferentialObject_obj_d · cited by 0Functor.mapDifferentialOb…CategoryTheory.DifferentialObject.d_squared_apply_assoc · cited by 0DifferentialObject.d_squa…HomologicalComplex.homologicalComplexToDGO_obj_d · cited by 0HomologicalComplex.homolo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.shiftFunctor · cited by 1553CategoryTheory.shiftFunct…CategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftAddMonoidWithOne · cited by 313AddMonoidWithOneCategoryTheory.DifferentialObject · cited by 61CategoryTheory.Differenti…CategoryTheory.DifferentialObject.obj · cited by 50DifferentialObject.objDifferentialObject.dCITED BYCITES

Cites9

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Cited by33

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