ofOrderIso — Mathlib

English

Given an order isomorphism e: J′ ≃o J, the underlying isomorphism aligns the bottom components of the transfinite composition.

Русский

При наличии изоморфизма порядка e: J′ ≃o J соответствующее основание композиции согласуется под изоморфизмом.

LaTeX

$$$\text{IsColimit alignment under } e$ for TransfiniteCompositionOfShape$$

Lean4

/-- If `f` is a transfinite composition of shape `J`, then it is
also a transfinite composition of shape `J'` if `J' ≃o J`. -/
@[simps]
def ofOrderIso {J' : Type w'} [LinearOrder J'] [OrderBot J'] [SuccOrder J'] [WellFoundedLT J'] (e : J' ≃o J) :
    TransfiniteCompositionOfShape J' f where
  F := e.equivalence.functor ⋙ c.F
  isoBot := c.F.mapIso (eqToIso e.map_bot) ≪≫ c.isoBot
  incl := Functor.whiskerLeft e.equivalence.functor c.incl
  isColimit := IsColimit.whiskerEquivalence (c.isColimit) e.equivalence

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