By embedding Uq(sl2) into the path coalgebra , where
is the Gabriel quiver of Uq(sl2) as a coalgebra, we obtain a basis of Uq(sl2) in terms of combinations of paths of the quiver
; this special basis enables us to describe the category of Uq(sl2)-comodules by certain representations of
; and this description further permits us to construct a class of modules of SLq(2), from certain representations of
, via the duality between Uq(sl2) and SLq(2).