Theorems · Definition · category theory

CategoryTheory.ShortComplex.homMk

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} →
        (τ₁ : S₁.X₁ ⟶ S₂.X₁) →
          (τ₂ : S₁.X₂ ⟶ S₂.X₂) →
            (τ₃ : S₁.X₃ ⟶ S₂.X₃) →
              CategoryTheory.CategoryStruct.comp τ₁ S₂.f = CategoryTheory.CategoryStruct.comp S₁.f τ₂ →
                CategoryTheory.CategoryStruct.comp τ₂ S₂.g = CategoryTheory.CategoryStruct.comp S₁.g τ₃ → (S₁ ⟶ S₂)

A constructor for morphisms in ShortComplex C when the commutativity conditions are not obvious.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Basic

Cited by

11 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms