Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A bivariant Yoneda lemma and $(\infty,2)$-categories of correspondences   Everyone knows that if you have a bivariant homology theory satisfying a base
change formula, you get an representation of a category of correspondences. For
theories in which the covariant and contravariant transfer maps are in mutual
adjunction, these data are actually equivalent. In other words, a 2-category of
correspondences is the universal way to attach to a given 1-category a set of
right adjoints that satisfy a base change formula.
  Through a bivariant version of the Yoneda paradigm, I give a definition of
correspondences in higher category theory and prove an extension theorem for
bivariant functors. Moreover, conditioned on the existence of a 2-dimensional
Grothendieck construction, I provide a proof of the aforementioned universal
property. The methods, morally speaking, employ the `internal logic' of higher
category theory: they make no explicit use of any particular model.

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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph