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Nguyen Tien Quang

  1. On monoidal functors between (braided) Gr-categories.

    Fri, 05/27/2011 - 15:01 — SomNambul
    Authors: Nguyen Tien Quang, Nguyen Thu Thuy, Pham Thi Cuc
    Subjects: Category Theory
    Abstract

    In this paper, we state and prove precise theorems on the classification of
    the category of (braided) categorical groups and their (braided) monoidal
    functors, and some applications obtained from the basic studies on monoidal
    functors between categorical groups.

  2. Cohomological Classification of Ann-categories.

    Fri, 05/27/2011 - 15:01 — SomNambul
    Authors: Nguyen Tien Quang
    Subjects: Category Theory
    Abstract

    The notion of Ann-categories is a categorification of the ring structure.
    Regular Ann-categories were classified by Shukla algebraic cohomology. In this
    article, we state and prove the precise theorem on classification for the
    general case due to Mac Lane cohomology for rings. And an application for
    classification problem of ring extensions is also introduced.

  3. Duals of Ann-categories.

    Tue, 09/07/2010 - 15:01 — SomNambul
    Authors: Nguyen Tien Quang, Dang Dinh hanh
    Subjects: Category Theory
    Abstract

    Dual 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.

  4. On the braiding of an Ann-category.

    Wed, 09/09/2009 - 22:08 — SomNambul
    Authors: Nguyen Tien Quang, Dang Dinh hanh
    Subjects: Category Theory
    Abstract

    A 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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