whiskerToCone — Mathlib

English

Taking the cone of a whiskered bicone is isomorphic to whiskering the cone and postcomposing with an isomorphism.

Русский

Переход к конусу через whiskered биконе является полным равенством конусов и пост-композицией с изоморфизмом.

LaTeX

$$$$ (c.whisker g).toCone \\cong (Cones.postcompose (Discrete.functorComp f g).inv).obj (c.toCone.whisker (Discrete.functor (Discrete.mk \\circ g))). $$$$

Lean4

/-- Taking the cone of a whiskered bicone results in a cone isomorphic to one gained
by whiskering the cone and postcomposing with a suitable isomorphism. -/
def whiskerToCone {f : J → C} (c : Bicone f) (g : K ≃ J) :
    (c.whisker g).toCone ≅
      (Cones.postcompose (Discrete.functorComp f g).inv).obj (c.toCone.whisker (Discrete.functor (Discrete.mk ∘ g))) :=
  Cones.ext (Iso.refl _) (by simp)

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