pentagon — Mathlib

English

Another form of the pentagon identity in functor calculus: a detailed equality of compositions built from associators and whiskers showing coherence of associativity.

Русский

Другая форма пентагональной когерентности в вычислении функторов.

LaTeX

$$$\\text{pentagon equality with whiskers: }$ (expression involving associators and whiskers).$$

Lean4

theorem pentagon :
    whiskerRight (associator F G H).hom K ≫ (associator F (G ⋙ H) K).hom ≫ whiskerLeft F (associator G H K).hom =
      (associator (F ⋙ G) H K).hom ≫ (associator F G (H ⋙ K)).hom :=
  by cat_disch

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