instCofibrationInlOfIsCofibrant — Mathlib

English

In a category with cofibrations respecting isomorphisms, for any arrow i : A → X with A initial, IsCofibrant X is equivalent to Cofibration i.

Русский

В категории с кофибриками, сохраняющими изоморфности, при любом стрелке i : A → X с A начальным, IsCofibrant X эквивалентно Cofibration i.

LaTeX

$$IsCofibrant X ↔ Cofibration i$$

Lean4

instance [hY : IsCofibrant Y] : Cofibration (coprod.inl : X ⟶ X ⨿ Y) :=
  by
  rw [isCofibrant_iff] at hY
  rw [cofibration_iff] at hY ⊢
  exact
    MorphismProperty.of_isPushout
      ((IsPushout.of_isColimit_binaryCofan_of_isInitial (colimit.isColimit (pair X Y)) initialIsInitial).flip) hY

Похожие утверждения