In [the paper]( http://people.maths.ox.ac.uk/~laugwitz/2010-08%20-%20Yetter-Drinfeld%20and%20Hopf%20Modules%20-%20Bachelorarbeit.pdf ), page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is 
$$
h_{(1)}.v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H.
$$ 
On the other hand, in [the article](https://en.wikipedia.org/wiki/Yetter%E2%80%93Drinfeld_category#Definition), the compatibility condition for a Yetter-Drinfeld module over $H$ is 
$$
\delta(h.v) = h_{(1)} v_{(-1)} S(h_{(3)}) \otimes h_{(2)}.v_{(0)}, v \in V, h \in H.
$$ 
Are the two conditions equivalent? Thank you very much.