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Structure of Ann-categories

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 نشر من قبل Tien Quang Nguyen
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English
 تأليف Nguyen Tien Quang




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Each Ann-category $A$ is equivalent to an Ann-category of the type $(R,M),$ where $M$ is an $R$-bimodule. The family of constraints of $A$ induces a {it structure} on $(R,M).$ The main result of the paper is: 1. {it There exists a bijection between the set of structures on $(R,M)$ and the group of Mac Lane 3-cocycles $Z^{3}_{MaL}(R, M).$} 2. {it There exists a bijection between $C(R,M)$ of congruence classes of Ann-categories whose pre-stick is of the type $(R,M)$ and the Mac Lane cohomology group $H^3_{textrm{MaL}}(R,M).$}



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