Theorems · Definition · category theory

CategoryTheory.ShortComplex.isoMk

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} →
        (e₁ : S₁.X₁ ≅ S₂.X₁) →
          (e₂ : S₁.X₂ ≅ S₂.X₂) →
            (e₃ : S₁.X₃ ≅ S₂.X₃) →
              autoParam
                  (CategoryTheory.CategoryStruct.comp e₁.hom S₂.f = CategoryTheory.CategoryStruct.comp S₁.f e₂.hom)
                  CategoryTheory.ShortComplex.isoMk._auto_1 →
                autoParam
                    (CategoryTheory.CategoryStruct.comp e₂.hom S₂.g = CategoryTheory.CategoryStruct.comp S₁.g e₃.hom)
                    CategoryTheory.ShortComplex.isoMk._auto_3 →
                  (S₁ ≅ S₂)

A constructor for isomorphisms in the category ShortComplex C

Defined in

Mathlib.Algebra.Homology.ShortComplex.Basic

Cited by

30 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms