Abstract
Let C be a cocomplete monoidal category such that the tensor product in C preserves colimits in each argument. Let A be an algebra in C . We show (under some assumptions including “faithful flatness” of A) that the center of the monoidal category ( A C A,⊗ A) of A– A-bimodules is equivalent to the center of C (hence in a sense trivial): Z( A C A)≅ Z( C) . Assuming A to be a commutative algebra in the center Z( C) , we compute the center Z( C A) of the category of right A-modules (considered as a subcategory of A C A using the structure of A∈ Z( C) . We find Z( C A)≅ dys Z( C) A , the category of dyslectic right A-modules in the braided category Z( C) .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
