|
This article is cited in 1 scientific paper (total in 1 paper)
Mathematical logic, algebra and number theory
Extensions of the category $S-Act$
E. E. Skurikhinab, A. A. Stepanovab, A. G. Sukhonosb a Institute of Applied Mathematics, 7, Radio str., Vladivostok, 690041, Russia
b Far-Eastern Federal University, 10, Ajax Bay, Russky Island, Vladivostok, 690920, Russia
Abstract:
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.
Received October 20, 2021, published November 23, 2021
Citation:
E. E. Skurikhin, A. A. Stepanova, A. G. Sukhonos, “Extensions of the category $S-Act$”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1332–1357
Linking options:
https://www.mathnet.ru/eng/semr1443 https://www.mathnet.ru/eng/semr/v18/i2/p1332
|
Statistics & downloads: |
Abstract page: | 108 | Full-text PDF : | 33 | References: | 12 |
|