factorThruImage_comp_coimageIsoImage'_inv

English

The composition factorThruImage f ≫ (coimageIsoImage' f).inv equals cokernel.π f’s kernel π, i.e., kernel.ι f.

Русский

Составление factorThruImage f затем (coimageIsoImage' f)^{-1} равно kernel.ι f как кокernel-порожденная.

LaTeX

$$$$ \\operatorname{factorThruImage} f \\;\\circ\\; (\\operatorname{coimageIsoImage}' f)^{-1} = \\operatorname{kernel}.\\pi( f ) $$$$

Lean4

theorem factorThruImage_comp_coimageIsoImage'_inv : factorThruImage f ≫ (coimageIsoImage' f).inv = cokernel.π _ := by
  simp only [IsImage.isoExt_inv, image.isImage_lift, image.fac_lift, coimageStrongEpiMonoFactorisation_e]

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