Mathlib Map

Theorems · Definition · category theory

CategoryTheory.DifferentialObject.obj

{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] → CategoryTheory.DifferentialObject S C → C

The underlying object of a differential object.

Defined in
Mathlib.CategoryTheory.DifferentialObject
Cited by
50 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
AddMonoidWithOneCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShift
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.DifferentialObject.Hom.f · cited by 28Hom.fCategoryTheory.DifferentialObject.d · cited by 23DifferentialObject.dHomologicalComplex.dgoToHomologicalComplex · cited by 10HomologicalComplex.dgoToH…CategoryTheory.DifferentialObject.objEqToHom · cited by 8DifferentialObject.objEqT…CategoryTheory.DifferentialObject.shiftFunctor · cited by 7DifferentialObject.shiftF…CategoryTheory.DifferentialObject.isoApp · cited by 5DifferentialObject.isoAppCategoryTheory.DifferentialObject.mkIso · cited by 3DifferentialObject.mkIsoCategoryTheory.Functor.mapDifferentialObject · cited by 3Functor.mapDifferentialOb…HomologicalComplex.dgoEquivHomologicalComplexUnitIso · cited by 3HomologicalComplex.dgoEqu…CategoryTheory.DifferentialObject.d_squared · cited by 2DifferentialObject.d_squa…CategoryTheory.DifferentialObject.shiftFunctorAdd · cited by 2DifferentialObject.shiftF…CategoryTheory.DifferentialObject.shiftZero · cited by 2DifferentialObject.shiftZ…CategoryTheory.DifferentialObject.Hom.ext · cited by 2Hom.extCategoryTheory.DifferentialObject.d_squared_apply · cited by 1DifferentialObject.d_squa…CategoryTheory.DifferentialObject.eqToHom_f' · cited by 1DifferentialObject.eqToHo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftAddMonoidWithOne · cited by 313AddMonoidWithOneCategoryTheory.DifferentialObject · cited by 61CategoryTheory.Differenti…DifferentialObject.objCITED BYCITES

Cites5

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

Cited by69

Results whose statement or proof uses this declaration.