English
There is a canonical chain map from the truncation of a cochain complex to the single-object cochain complex in degree 0.
Русский
Существует каноничское цепное отображение от усечения ко chain complex к однообъектному коцепному комплексa в нулевой степени.
LaTeX
$$$\\text{toTruncate}(C) : (\\text{single}_0 V).X_0 \\to \\text{truncate}.C$ with the map given by $C.d_{0,1}$ in degree 0 and zero elsewhere.$$
Lean4
/-- There is a canonical chain map from the truncation of a cochain complex `C` to
the "single object" cochain complex consisting of the truncated object `C.X 0` in degree 0.
The components of this chain map are `C.d 0 1` in degree 0, and zero otherwise.
-/
def toTruncate [HasZeroObject V] [HasZeroMorphisms V] (C : CochainComplex V ℕ) :
(single₀ V).obj (C.X 0) ⟶ truncate.obj C :=
(fromSingle₀Equiv (truncate.obj C) (C.X 0)).symm ⟨C.d 0 1, by simp⟩
