Theorems · Definition · category theory

CategoryTheory.DifferentialObject.mkIso

{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} →
              (f : X.obj ≅ Y.obj) →
                CategoryTheory.CategoryStruct.comp X.d ((CategoryTheory.shiftFunctor C 1).map f.hom) =
                    CategoryTheory.CategoryStruct.comp f.hom Y.d →
                  (X ≅ Y)

An isomorphism of differential objects can be constructed from an isomorphism of the underlying objects that commutes with the differentials.

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.HasShift