Generalized S-Act Categories and Their Topos Structure

This paper introduces and studies two natural generalizations of the category S-Act: the category SS-Act and its reflective subcategory FS-Act. We show that SS-Act admits a full and faithful embedding into a Grothendieck topos. As a consequence, SS-Act is cartesian closed and has finite limits, while it fails to be complete or cocomplete in general. We further analyze limit constructions and show that SS-Act becomes complete and equivalent to Sets-Act when S is a group.

کلیدواژه ها:

S-system ، Grothendieck topos ، cartesian closed category ، monoid ، limit