Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Classification of Two-Dimensional Extended Topological Field
  Theories   We provide a complete generators and relations presentation of the
2-dimensional extended unoriented and oriented bordism bicategories as
symmetric monoidal bicategories. Thereby we classify these types of
2-dimensional extended topological field theories with arbitrary target
bicategory. As an immediate corollary we obtain a concrete classification when
the target is the symmetric monoidal bicategory of algebras, bimodules, and
intertwiners over a fixed commutative ground ring. In the oriented case, such
an extended topological field theory is equivalent to specifying a
(non-commutative) separable symmetric Frobenius algebra. The text is divided
into three chapters. The first develops a variant of higher Morse theory and
uses it to obtain a combinatorial description of surfaces suitable for the
higher categorical language used later. The second chapter is an extensive
treatment of the theory of symmetric monoidal bicategories. We introduce
several stricter variants on the notion of symmetric monoidal bicategory, and
give a very general treatment of the notion of presentation by generators and
relations. Finally we provide a host of strictification and cohernece results
for symmetric monoidal bicategories. The final chapter focuses on extended
tqfts. We give a precise treatment of the extended bordism bicategory equipped
with additional structure (such as framings or orientations). We apply the
results of the previous two chapters to obtain a simple presentation of both
the oriented and unoriented bordism bicategories, and describe the general
method to obtain such classifications for other choices of structure. We
examine the consequences of our classification when the target is the
bicategory of algebras, bimodules, and maps, over a fixed commutative ground
ring.

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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: cs