  Effective Burnside $\infty$-categories are the centerpiece of the
$\infty$-categorical approach to equivariant stable homotopy theory. In this
\'etude, we recall the construction of the twisted arrow $\infty$-category, and
we give a new proof that it is an $\infty$-category, using an extremely helpful
modification of an argument due to Joyal--Tierney. The twisted arrow
$\infty$-category is in turn used to construct the effective Burnside
$\infty$-category. We employ a variation on this theme to construct a fibrewise
effective Burnside $\infty$-category. To show that this constuctionworks
fibrewise, we introduce a fragment of a theory of what we call marbled
simplicial sets, and we use a yet further modified form of the Joyal--Tierney
argument.
