ι_reflexiveCoequalizerIsoCoequalizer_hom

English

The composition colimit.ι F 0 followed by reflexiveCoequalizerIsoCoequalizer.hom equals coequalizer.π (F.map left) (F.map right).

Русский

comp colimit.ι F zero затем reflexiveCoequalizerIsoCoequalizer.hom равно coequalizer.π (F.map left) (F.map right).

LaTeX

$$$\mathrm{colimit.\,ι}\,F\,0 \;\gg\; (\mathrm{reflexiveCoequalizerIsoCoequalizer}\,F).hom = \mathrm{coequalizer.\,\pi}(F.map\ left)(F.map\ right)$$$

Lean4

@[reassoc (attr := simp)]
theorem ι_reflexiveCoequalizerIsoCoequalizer_hom :
    colimit.ι F zero ≫ (reflexiveCoequalizerIsoCoequalizer F).hom = coequalizer.π (F.map left) (F.map right) :=
  IsColimit.comp_coconePointUniqueUpToIso_hom ((ReflexiveCofork.isColimitEquiv F _).symm _) _ WalkingParallelPair.one

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