hasCokernel_of_hasCoequalizer — Mathlib

English

If the cokernel of f − g is zero, then f and g have a coequalizer.

Русский

Если кокernel f − g равен нулю, то существуют кое-равнители f и g.

LaTeX

$$HasCokernel(f - g) ≅ 0 ⇒ HasCoequalizer(f, g)$$

Lean4

/-- A preadditive category has a cokernel for `f - g` if it has a coequalizer for `f` and `g`. -/
theorem hasCokernel_of_hasCoequalizer [HasCoequalizer f g] : HasCokernel (f - g) :=
  HasColimit.mk
    { cocone := cokernelCoforkOfCofork (coequalizer.cofork f g)
      isColimit := isColimitCokernelCoforkOfCofork (colimit.isColimit (parallelPair f g)) }

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