English
One can interchange mapWhiskerLeft and mapWhiskerRight with suitable arguments.
Русский
Можно поменять местами mapWhiskerLeft и mapWhiskerRight с подходящими аргументами.
LaTeX
$$$ mapWhiskerLeft F α \;\circ\; mapWhiskerRight β G = mapWhiskerRight α F \;\circ\; mapWhiskerLeft G β $$$
Lean4
/-- One can exchange `mapWhiskerLeft` and `mapWhiskerRight`. -/
theorem mapWhisker_exchange (Fₗ : C ⥤ E) (Gₗ : C ⥤ E) (Fᵣ : D ⥤ E') (Gᵣ : D ⥤ E') (αₗ : Fₗ ⟶ Gₗ) (αᵣ : Fᵣ ⟶ Gᵣ) :
mapWhiskerLeft Fₗ αᵣ ≫ mapWhiskerRight αₗ Gᵣ = mapWhiskerRight αₗ Fᵣ ≫ mapWhiskerLeft Gₗ αᵣ :=
by
ext
cat_disch