kernelSubobjectMap — Mathlib

English

kernelSubobjectMap of the identity on Arrow.mk f is the identity on kernelSubobject f.

Русский

map ядра подмножества от тождественного стрелы равен тождественному отображению ядра.

LaTeX

$$$$ kernelSubobjectMap (id\\; (Arrow.mk f)) = id $$$$

Lean4

/-- A commuting square induces a morphism between the kernel subobjects. -/
def kernelSubobjectMap (sq : Arrow.mk f ⟶ Arrow.mk f') : (kernelSubobject f : C) ⟶ (kernelSubobject f' : C) :=
  Subobject.factorThru _ ((kernelSubobject f).arrow ≫ sq.left) (kernelSubobject_factors _ _ (by simp))

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