Copower functors
Copower functors
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DOI：
10.1016/j.tcs.2008.09.057
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发表时间：
2009-03-17
影响因子：
1.1
通讯作者：
Gumm, H. Peter
中科院分区：
文献类型：
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作者：
Gumm, H. Peter
我们给出了[hp . p .]中两个较早构造的一般推广Gumm， T. Schroder， monoid标记跃迁系统，理论计算机科学电子笔记44(1)(2001)184-203]，产生了加权的共代数型函子，参考文献。这些系统的过渡标记是由可交换单阵M或完全半格L绘制的，过渡结构与标记上的代数结构相互作用。这里，我们证明了那些早期的签名函子实际上是一种更一般的构造的实例，由所谓的幂函子提供。举例来说，我们在由代数的变种V给出的范畴中实例化了这个函子。特别地，对于所有半群的变种G，或所有（不一定交换）单群的变种m，并且对于m任意单群，我们发现所得到的共幂函子m (G)，竖条-竖条（代表m (m)竖条-竖条）弱保留回调当且仅当m是等分的（代表m）。圆锥形和等分的)。最后，我们证明了共幂函子是全称的，即每一个忠实集函子都可以被看作是一个合适的共幂函子的实例。(C) 2008 Elsevier B.V.版权所有
We give a common generalization of two earlier constructions in [H.P. Gumm, T. Schroder, Monoid-labeled transition systems, Electronic Notes in Theoretical Computer Science 44 (1) (2001) 184-203], that yielded coalgebraic type functors for weighted, resp. fuzzy transition systems, Transition labels for these systems were drawn from a commutative monoid M or a complete semilattice L, with the transition structure interacting with the algebraic structure on the labels. Here, we show that those earlier signature functors are in fact instances of a more general construction, provided by the so-called copower functor.Exemplary, we instantiate this functor in categories given by varieties V of algebras. In particular, for the variety G of all semigroups, or the variety m of all (not necessarily commutative) monoids, and with M any monoid, we find that the resulting copower functors M(G), vertical bar-vertical bar (resp M(m)vertical bar-vertical bar) weakly preserve pullbacks if and only if M is equidivisible (resp. conical and equidivisible).Finally, we show that copower functors are universal in the sense that every faithful set-functor can be seen as an instance of an appropriate copower functor. (C) 2008 Elsevier B.V. All rights reserved.