Geodesic
Extensions of the category $S-Act$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1332-1357

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We define a new category $SS-Act$ whose objects are $S$-acts and whose morphisms are defined so that each set $Hom_{SS-Act}(A, B)$ is an $S$-act. It is proved that this category has a reflective subcategory $ FS-Act $ that is naturally isomorphic to the category $ S-Act $. The set $Hom_{FS-Act}(A,B)$ coincides with the set of all fixed points of the $S$-act $Hom_{SS-Act}(A,B)$. In the case when $S$ is a group, it is proved that the category $SS-Act$ is a Grothendieck topos and the construction of limits and colimits is considered.
Keywords: S-act, limits and colimits of functors, adjoint functor, Cartesian Closed Category. 
@article{SEMR_2021_18_2_a10,
     author = {E. E. Skurikhin and A. A. Stepanova and A. G. Sukhonos},
     title = {Extensions of the category $S-Act$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1332--1357},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a10/}
}
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E. E. Skurikhin; A. A. Stepanova; A. G. Sukhonos. Extensions of the category $S-Act$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1332-1357. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a10/