Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incidence bicomodules, M\"obius inversion, and a Rota formula for
  infinity adjunctions   In the same way decomposition spaces, also known as unital 2-Segal spaces,
have incidence (co)algebras, and certain relative decomposition spaces have
incidence (co)modules, we identify the structures that have incidence
bi(co)modules: they are certain augmented double Segal spaces subject to some
exactness conditions. We establish a M\"obius inversion principle for
(co)modules, and a Rota formula for certain more involved structures called
M\"obius bicomodule configurations. The most important instance of the latter
notion arises as mapping cylinders of infinity adjunctions, or more generally
of adjunctions between M\"obius decomposition spaces, in the spirit of Rota's
original formula.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph