  Galaxy properties primarily depend on their host halo mass. Halo mass, in
turn, depends on the cosmic web environment. We explore if the effect of the
cosmic web on galaxy properties is entirely transitive via host halo mass, or
if the cosmic web has an effect independent of mass. The secondary galaxy bias,
sometimes referred to as "galaxy assembly bias", is the beyond-mass component
of the galaxy-halo connection. We investigate the link between the cosmic web
environment and the secondary galaxy bias in simulations. We measure the
secondary galaxy bias through the following summary statistics: projected
two-point correlation function, $\wprp$, and counts-in-cylinders statistics,
$\Pncic$. First, we examine the extent to which the secondary galaxy bias can
be accounted for with a measure of the environment as a secondary halo
property. We find that the total secondary galaxy bias preferentially places
galaxies in more strongly clustered haloes. In particular, haloes at fixed mass
tend to host more galaxies when they are more strongly associated with nodes or
filaments. This tendency accounts for a significant portion, but not the
entirety, of the total secondary galaxy bias effect. Second, we quantify how
the secondary galaxy bias behaves differently depending on the host halo
proximity to nodes and filaments. We find that the total secondary galaxy bias
is relatively stronger in haloes more associated with nodes or filaments. We
emphasise the importance of removing halo mass effects when considering the
cosmic web environment as a factor in the galaxy-halo connection.
