Dang Dinh hanh
Duals of Ann-categories.
Tue, 09/07/2010 - 15:01 — SomNambulAuthors: Nguyen Tien Quang, Dang Dinh hanh
Subjects: Category Theory
AbstractDual monoidal category $\mathcal C^\ast$ of a monoidal functor $F:\mathcal
C\to \mathcal V$ has been constructed by S. Majid. In this paper, we extend the
construction of dual structures for an Ann-functor $F:\mathcal B\to \mathcal
A$. In particular, when $F=id_{\mathcal A}$, then the dual category $\mathcal
A^{\ast}$ is indeed the center of $\mathcal A$ and this is a braided
Ann-category.On the braiding of an Ann-category.
Wed, 09/09/2009 - 22:08 — SomNambulAuthors: Nguyen Tien Quang, Dang Dinh hanh
Subjects: Category Theory
AbstractA braided Ann-category $\A$ is an Ann-category $\A$ together with the
braiding $c$ such that $(\A, \otimes, a, c, (I,l,r))$ is a braided tensor
category, and $c$ is compatible with the distributivity constraints. The paper
shows the dependence of the left (or right) distributivity constraint on other
axioms. Hence, the paper shows the relation to the concepts of {\it
distributivity category} due to M. L. Laplaza and {\it ring-like category} due
to A. Frohlich and C.T.C Wall.
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