mapWhiskerLeft_rightUnitor_hom — Mathlib

English

The whiskering map composition with associator on the left satisfies a naturality relation with mapWhiskerLeft and mapCompRight.

Русский

Сочетание whiskerLeft и ассоциатора слева удовлетворяет естественной связи с mapWhiskerLeft и mapCompRight.

LaTeX

$$$\operatorname{mapWhiskerLeft}\_ (F \!\! \!\! \text{associator } G H)^{\mathrm{hom}} = (\operatorname{mapCompRight} A (F \!\! \! \! G) H)^{\mathrm{hom}} \;\circ \; \mathrm{whiskerRight}(\operatorname{mapCompRight} A F G)^{\mathrm{hom}} (\operatorname{mapPair} (\mathbf{1}_A) H)\; \circ \cdots$$$

Lean4

theorem mapWhiskerLeft_rightUnitor_hom (F : B ⥤ C) :
    mapWhiskerLeft _ F.rightUnitor.hom =
      (mapCompRight A F (𝟭 C)).hom ≫ whiskerLeft (mapPair _ F) mapPairId.hom ≫ (mapPair (𝟭 A) _).rightUnitor.hom :=
  by apply natTrans_ext <;> ext <;> simp [mapCompRight]

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