Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fibrewise effective Burnside $\infty$-category   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.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci