Smash Product of Semigroup-Graded Category
Qinghua Chen · Journal of Huaqiao University · 2008
For Smash product of semigroup-graded category,we prove that the quotient category(C#S)/S of Smash product C#S of semigroup S graded category C is isomorphic to category C,and the Smash product category(B/S)#S of the quotient category B/S of free semigroup S category B is isomorphic to category B when S is a cancellative semigroup with identity 1.It is shown that the semigroup-graded categorical Smash product and the semigroup categorical quotient are inverse structions between semigroup-graded categories and free semigroup action categories.