Frontiers of Mathematics in China >
Map composition generalized to coherent collections of maps
Received date: 09 Oct 2013
Accepted date: 16 Sep 2014
Published date: 01 Apr 2015
Copyright
Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with every point in the domain associated with a special set of maps. Polymaps can be represented as small subcategories of Set∗, the category of pointed sets. Map composition and the counterpart of relation union for maps are generalized to polymap composition and sum. Algebraic structures and categories of polymaps are investigated. Polymaps present the unique perspective of an algebra that can retain many of its properties when its elements (maps) are augmented with collections of other elements.
Key words： Relation algebra; partial algebra; composition
Herng Yi CHENG , Kang Hao CHEONG . Map composition generalized to coherent collections of maps[J]. Frontiers of Mathematics in China, 2015 , 10(3) : 547 -565 . DOI: 10.1007/s11464-015-0435-5
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