Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Varieties of Metric and Quantitative Algebras   Metric algebras are metric variants of $\Sigma$-algebras. They are first
introduced in the field of universal algebra to deal with algebras equipped
with metric structures such as normed vector spaces. Recently a similar notion
of quantitative algebra is used in computer science to formulate computational
effects of probabilistic programs. In this paper we show that varieties of
metric algebras (classes defined by a set of metric equations) are exactly
classes closed under (metric versions of) subalgebras, products and quotients.
This result implies the class of normed vector spaces cannot be defined by
metric equations, differently from the classical case where the class of vector
spaces is equational. This phenomenon suggests that metric equations are not a
very natural class of formulas since they cannot express such a typical class
of metric algebras. Therefore we need a broader class of formulas to acquire an
appropriate metric counterpart of the classical variety theory.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th