whisker — Mathlib

English

Whiskering a bilimit by an equivalence yields an equivalence of bilimit structure.

Русский

Whisker билилимита эквивалентности порождает эквивалентность структуры билилимита.

LaTeX

$$$$ (c.whisker g).IsBilimit \\equiv c.IsBilimit. $$$$

Lean4

/-- Whisker a bicone with an equivalence between the indexing types. -/
@[simps]
def whisker {f : J → C} (c : Bicone f) (g : K ≃ J) : Bicone (f ∘ g)
    where
  pt := c.pt
  π k := c.π (g k)
  ι k := c.ι (g k)
  ι_π k
    k' := by
    simp only [c.ι_π]
    split_ifs with h h' h' <;> simp [Equiv.apply_eq_iff_eq g] at h h' <;> tauto

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