cast — Mathlib

English

There is an isomorphism between SelfLERadical constructions when radical equality holds and a colimit construction.

Русский

Существует изоморфизм между конструкциями SelfLERadical при равенстве радикалов и конструкцией предела.

LaTeX

$$isoOfSameRadical (hJK) i$$

Lean4

/-- Casting from the full subcategory of ideals with radical containing `J` to the full
subcategory of ideals with radical containing `K`. -/
def cast (hJK : J.radical = K.radical) : SelfLERadical J ⥤ SelfLERadical K :=
  ObjectProperty.ιOfLE fun L hL => by
    rw [← Ideal.radical_le_radical_iff] at hL ⊢
    exact hJK.symm.trans_le hL

Похожие утверждения