Theorems · Definition · category theory

CategoryTheory.Functor.mapDifferentialObject

{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] →
            (D : Type u') →
              [inst_4 : CategoryTheory.Category.{v', u'} D] →
                [inst_5 : CategoryTheory.Limits.HasZeroMorphisms D] →
                  [inst_6 : CategoryTheory.HasShift D S] →
                    (F : CategoryTheory.Functor C D) →
                      ((CategoryTheory.shiftFunctor C 1).comp F ⟶ F.comp (CategoryTheory.shiftFunctor D 1)) →
                        (∀ (c c' : C), F.map 0 = 0) →
                          CategoryTheory.Functor (CategoryTheory.DifferentialObject S C)
                            (CategoryTheory.DifferentialObject S D)

A functor F : C ⥤ D which commutes with shift functors on C and D and preserves zero morphisms can be lifted to a functor DifferentialObject S C ⥤ DifferentialObject S D.

Defined in

Mathlib.CategoryTheory.DifferentialObject

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidWithOneCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShiftCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShift