factorThruKernelSubobject_comp_arrow

English

Composing factorThrough with kernelSubobjectIso hom yields kernel.lift: factorThruKernelSubobject f h w ≫ (kernelSubobjectIso f).hom = kernel.lift f h w.

Русский

Сочетание factorThrough с гомоморфизмом из kernelSubobjectIso даёт kernel.lift.

LaTeX

$$$$ factorThruKernelSubobject\\ f\\ h\\ w \\;\\gg (kernelSubobjectIso f).hom = kernel.lift f h w $$$$

Lean4

@[simp]
theorem factorThruKernelSubobject_comp_arrow {W : C} (h : W ⟶ X) (w : h ≫ f = 0) :
    factorThruKernelSubobject f h w ≫ (kernelSubobject f).arrow = h :=
  by
  dsimp [factorThruKernelSubobject]
  simp

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