Theorems · Theorem · category theory

HomologicalComplex.Hom.mk.injEq

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {A B : HomologicalComplex V c}
  (f : (i : ι) → A.X i ⟶ B.X i)
  (comm' :
    autoParam
      (∀ (i j : ι),
        c.Rel i j →
          CategoryTheory.CategoryStruct.comp (f i) (B.d i j) = CategoryTheory.CategoryStruct.comp (A.d i j) (f j))
      HomologicalComplex.Hom.comm'._autoParam)
  (f_1 : (i : ι) → A.X i ⟶ B.X i)
  (comm'_1 :
    autoParam
      (∀ (i j : ι),
        c.Rel i j →
          CategoryTheory.CategoryStruct.comp (f_1 i) (B.d i j) = CategoryTheory.CategoryStruct.comp (A.d i j) (f_1 j))
      HomologicalComplex.Hom.comm'._autoParam),
  ({ f := f, comm' := comm' } = { f := f_1, comm' := comm'_1 }) = (f = f_1)

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms