RELATION LIFTING, WITH AN APPLICATION TO THE MANY-VALUED COVER MODALITY
RELATION LIFTING, WITH AN APPLICATION TO THE MANY-VALUED COVER MODALITY
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DOI：
10.2168/lmcs-9(4:8)2013
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发表时间：
2013-01-01
影响因子：
0.6
通讯作者：
Velebil, Jiri
中科院分区：
文献类型：
--
作者：
Bilkova, Marta;Kurz, Alexander;Velebil, Jiri
我们介绍的基本概念和结果关系提升的范畴丰富的交换Quantale。本文给出了2-函子T允许函关系提升的两个充要条件：一是T在范畴上的幂集单子上的分配律的存在，二是T保持某些平方的正合性。这两个特征是概括的“经典”的结果集函子：第一个特征概括的存在分配律的真正幂集单子，第二个概括的保存弱回调。本文提出的结果使我们能够计算谓词拟合endofunctors例如，广义fultrajmetric空间。我们说明了这一点，通过研究在这种情况下的coalgebraic覆盖模态。
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the "powerset monad" on categories, one is the preservation by T of "exactness" of certain squares. Both characterisations are generalisations of the "classical" results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate fittings of endofunctors of for example, generalised fultrajmetric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.