Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waldhausen Additivity: Classical and Quasicategorical   We use a simplicial product version of Quillen's Theorem A to prove classical
Waldhausen Additivity of wS., which says that the "subobject" and "quotient"
functors of cofiber sequences induce a weak equivalence wS.E(A,C,B)--> wS.A x
wS.B . A consequence is Additivity for the Waldhausen K-theory spectrum of the
associated split exact sequence, namely a stable equivalence of spectra
K(A)vK(B)--> K(E(A,C,B)). This paper is dedicated to transferring these proofs
to the quasicategorical setting and developing Waldhausen quasicategories and
their sequences. We also give sufficient conditions for a split exact sequence
to be equivalent to a standard one. These conditions are always satisfied by
stable quasicategories, so Waldhausen K-theory sends any split exact sequence
of pointed stable quasicategories to a split cofiber sequence. Presentability
is not needed. In an effort to make the article self-contained, we recall all
the necessary results from the theory of quasicategories, and prove a few
quasicategorical results that are not in the literature.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex