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Lax distributive laws for topology, II
Theory and applications of categories, Tome 32 (2017), pp. 736-768 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18C15, 18C20, 18D99
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 
@article{TAC_2017_32_a20,
     author = {Hongliang Lai and Lili Shen and Walter Tholen},
     title = {Lax distributive laws for topology, {II}},
     journal = {Theory and applications of categories},
     pages = {736--768},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a20/}
}
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Hongliang Lai; Lili Shen; Walter Tholen. Lax distributive laws for topology, II. Theory and applications of categories, Tome 32 (2017), pp. 736-768. http://geodesic.mathdoc.fr/item/TAC_2017_32_a20/