Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Codensity Lifting of Monads and its Dual   We introduce a method to lift monads on the base category of a fibration to
its total category. This method, which we call codensity lifting, is applicable
to various fibrations which were not supported by its precursor, categorical
TT-lifting. After introducing the codensity lifting, we illustrate some
examples of codensity liftings of monads along the fibrations from the category
of preorders, topological spaces and extended pseudometric spaces to the
category of sets, and also the fibration from the category of binary relations
between measurable spaces. We also introduce the dual method called density
lifting of comonads. We next study the liftings of algebraic operations to the
codensity liftings of monads. We also give a characterisation of the class of
liftings of monads along posetal fibrations with fibred small meets as a limit
of a certain large diagram.

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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph