Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Varieties of Metric and Quantitative Algebras   A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first
introduced in universal algebra to deal with algebras equipped with metric
structures such as normed vector spaces. In this paper, we showed metric
versions of the variety theorem, which characterizes strict varieties (classes
of metric algebras defined by metric equations) and continuous varieties
(classes defined by a continuous family of basic quantitative inferences) by
means of closure properties. To this aim, we introduce the notion of
congruential pseudometric on a metric algebra, which corresponds to congruence
in classical universal algebra, and we investigate its structure.

24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph