, and Ross Street
, and Ross Street
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和罗斯街
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发表时间：
2005
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通讯作者：
Weinstein Sp
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作者：
C. Aw;Weinstein Sp
这项工作的目的是突出的概念，宽松的编织和宽松的monoidal类别的中心，更普遍的promonoidal类别。松弛的中心是松弛的编织。一般的中心是一个完整的子范畴的宽松中心，但我们表明，它有时是两个重合的情况。我们确定宽松的中心monoidal函范畴在各种情况下。Monoidal范畴的编织在[JS 1]及其前身中引入。在证明自由挠幺半群范畴具有另一个泛性质的过程中，[JS 0]引入了幺半群范畴X的中心ZX。一个monoidal范畴的中心是一个braided monoidal范畴。我们现在称之为松散的辫子，Yetter [Yet]认为是切题的。我们现在所说的X的松弛中心ZlX被P. Schauenburg [Sch]认为是“弱中心”。本工作的目的是强调松弛编织和松弛中心的概念monoidal类别X和更一般的promonoidal类别C。松弛中心是松弛辫幺半群范畴。一般来说，中心是松弛中心的一个完全子范畴，但有时两者重合。在不同的假设下，我们有两个这样的定理，一个是在加法上下文中存在足够的对偶对象的情况下，另一个是在加法上下文中。对于Promonoidal范畴C，我们将C上[Day]卷积的松弛中心与C的松弛中心上的卷积联系起来。事实上，有时它们是等同的。对X的松弛中心感兴趣的一个原因是，如果X的一个对象X在ZlX中具有幺半群的结构，那么对X进行张量定义了X的一个幺半群内函子− X ;这在松弛中心可以明确识别的情况下有应用。1991年数学学科分类。小学18 D10;中学18 D20、16 W30、20 L17。
The purpose of this work is to highlight the notions of lax braiding and lax centre for monoidal categories and more generally for promonoidal categories. Lax centres are lax braided. Generally the centre is a full subcategory of the lax centre, however we show that it is sometimes the case that the two coincide. We identify lax centres of monoidal functor categories in various cases. Introduction Braidings for monoidal categories were introduced in [JS1] and its forerunners. The centre ZX of a monoidal category X was introduced in [JS0] in the process of proving that the free tortile monoidal category has another universal property. The centre of a monoidal category is a braided monoidal category. What we now call lax braidings were considered tangentially by Yetter [Yet]. What we now call the lax centre ZlX of X was considered under the name “weak centre” by P. Schauenburg [Sch]. The purpose of this work is to highlight the notions of lax braiding and lax centre for monoidal categories X and more generally for promonoidal categories C . Lax centres turn out to be lax braided monoidal categories. Generally the centre is a full subcategory of the lax centre, however it is sometimes the case that the two coincide. We have two such theorems under different hypotheses, one in the case sufficient dual objects exist in the additive context, and the other in the cartesian context. For a promonoidal category C , we relate the lax centre of the [Day] convolution on C to the convolution on the lax centre of C . Indeed, sometimes these are equivalent. One reason for being interested in the lax centre of X is that, if an object X of X is equipped with the structure of monoid in ZlX , then tensoring with X defines a monoidal endofunctor −⊗X of X ; this has applications in cases where the lax centre can be explicitly identified. 1991 Mathematics Subject Classification. Primary 18D10; Secondary 18D20, 16W30, 20L17.