Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant monads and equivariant lifts versus a 2-category of
  distributive laws   Fix a monoidal category C. The 2-category of monads in the 2-category of
C-actegories, colax C-equivarant functors, and C-equivariant natural
transformations of colax functors, may be recast in terms of pairs consisting
of a usual monad and a distributive law between the monad and the action of C,
morphisms of monads respecting the distributive law, and transformations of
monads satisfying some compatibility with the actions and distributive laws
involved. The monads in this picture may be generalized to actions of monoidal
categories, and actions of PRO-s in particular. If C is a PRO as well, then in
special cases one gets various distributive laws of a given classical type, for
example between a comonad and an endofunctor or between a monad and a comonad.
The usual pentagons are in general replaced by multigons, and there are also
``mixed'' multigons involving two distinct distributive laws. Beck's bijection
between the distributive laws and lifts of one monad to the Eilenberg-Moore
category of another monad is here extended to an isomorphism of 2-categories.
The lifts of maps of above mentioned pairs are colax C-equivariant. We finish
with a short treatment of relative distributive laws between two pseudoalgebra
structures which are relative with respect to the distributivity of two
pseudomonads involved, what gives a hint toward the generalizations.

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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex