English
The functorial action on morphisms for the opposite-structured functor from WidePullbackShape to WidePushoutShape is given by mapping id to id and term to init.
Русский
Действие на морфизмы у противоположного живого функторa от WidePullbackShape к WidePushoutShape задаётся так: для гомоморфизмов id идёт в id, а для term идёт в init.
LaTeX
$$$\\text{widePullbackShapeOpMap} : X \\to Y \\mapsto ...$ (описание соответствует выше)$$
Lean4
/-- The action on morphisms of the obvious functor
`WidePullbackShape_op : WidePullbackShape J ⥤ (WidePushoutShape J)ᵒᵖ` -/
def widePullbackShapeOpMap :
∀ X Y : WidePullbackShape J, (X ⟶ Y) → ((op X : (WidePushoutShape J)ᵒᵖ) ⟶ (op Y : (WidePushoutShape J)ᵒᵖ))
| _, _, WidePullbackShape.Hom.id X => Quiver.Hom.op (WidePushoutShape.Hom.id _)
| _, _, WidePullbackShape.Hom.term _ => Quiver.Hom.op (WidePushoutShape.Hom.init _)
