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Lax distributive laws for topology, II

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Hongliang Lai, Lili Shen and Walter Tholen

For a small quantaloid Q we consider four fundamental 2-monads
T on Q-**Cat**, given by the presheaf
2-monad P and the copresheaf 2-monad P^{\dagger}, as
well as by their two composite 2-monads, and establish that they all laxly
distribute over P. These four 2-monads therefore admit lax
extensions to the category Q-**Dist** of
Q-categories and their distributors. We characterize the
corresponding (T,Q)-categories in each of the four
cases, leading us to both known and novel categorical structures.

Keywords:
quantaloid, monad, presheaf monad, copresheaf monad, double
presheaf monad, double copresheaf monad, lax distributive law, lax
$\lambda$-algebra, lax monad extension, Q-closure space,
Q-interior space

2010 MSC:
18C15, 18C20, 18D99

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 21, pp 736-768.

Published 2017-07-11.

http://www.tac.mta.ca/tac/volumes/32/21/32-21.pdf

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