Theorems · Theorem · category theory

HomologicalComplex.Hom.mk.congr_simp

∀ {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 f_1 : (i : ι) → A.X i ⟶ B.X i) (e_f : f = f_1)
  (comm' :
    ∀ (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)),
  { f := f, comm' := comm' } = { f := f_1, comm' := ⋯ }

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

2 results in Mathlib

Foundations

Depth 10 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms