Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diversities and Conformities   Diversities have recently been developed as multiway metrics admitting clear
and useful notions of hyperconvexity and tight span. In this note we consider
the analytic properties of diversities, in particular the generalizations of
uniform continuity, uniform convergence, Cauchy sequences and completeness to
diversities. We develop conformities, a diversity analogue of uniform spaces,
which abstract these concepts in the metric case. We show that much of the
theory of uniform spaces admits a natural analogue in this new structure; for
example, conformities can be defined either axiomatically or in terms of
uniformly continuous pseudodiversities.
  Just as diversities can be restricted to metrics, conformities can be
restricted to uniformities. We find that these two notions of restriction,
which are functors in the appropriate categories, are related by a natural
transformation.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph