homotopy_congruence — Mathlib

English

The quotient functor from homotopic complexes to the quotient category is full, i.e., every morphism in the quotient is the image of a morphism upstairs.

Русский

Частный functor квоты от гомотопических комплексов к квоти-категории — полнота: любой морфизм в квоти исходит как образ морфизма вверх по точкам.

LaTeX

$$$\text{Full}((\text{quotient } V c))$$$

Lean4

instance homotopy_congruence : Congruence (homotopic V c)
    where
  equivalence :=
    { refl := fun C => ⟨Homotopy.refl C⟩
      symm := fun ⟨w⟩ => ⟨w.symm⟩
      trans := fun ⟨w₁⟩ ⟨w₂⟩ => ⟨w₁.trans w₂⟩ }
  compLeft := fun _ _ _ ⟨i⟩ => ⟨i.compLeft _⟩
  compRight := fun _ ⟨i⟩ => ⟨i.compRight _⟩

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