Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary characterisation of sifted weights   Sifted colimits (those that commute with finite products in sets) play a
major role in categorical universal algebra. For example, varieties of
(many-sorted) algebras are precisely the free cocompletions under sifted
colimits of (many-sorted) Lawvere theories. Such a characterisation does not
depend on the existence of finite products in algebraic theories, but on the
above fact that these products commute with sifted colimits and another
condition: finite products form a sound class of limits.
  In this paper we study the notion of soundness for general classes of weights
in enriched category theory. We show that soundness of a given class of weights
is equivalent to having a `nice' characterisation of flat weights for that
class. As an application, we give an elementary characterisation of sifted
weights for the enrichment in categories and in preorders. We also provide a
number of examples of sifted weights using our elementary criterion.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an