Theorems · Theorem · category theory

HomologicalComplex.Hom.mk.inj

∀ {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

1 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms