English
Whiskering a natural transformation with a functor preserves the equivalence structure between NatTrans and HomObj.
Русский
Взвешивание естественного преобразования с функтором сохраняет эквивалентность между NatTrans и HomObj.
LaTeX
$$WhiskerLeft and WhiskerRight compatibilities for natTransEquiv$$
Lean4
theorem leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom (X : D)
(f : CostructuredArrow L X) :
(leftKanExtensionUnit L F).app f.left ≫
(leftKanExtension L F).map f.hom ≫ (L.leftKanExtensionObjIsoColimit F X).hom =
colimit.ι (proj L X ⋙ F) f :=
LeftExtension.IsPointwiseLeftKanExtensionAt.ι_isoColimit_hom (F := F)
(isPointwiseLeftKanExtensionLeftKanExtensionUnit L F X) f
