Map composition generalized to coherent collections of maps

doi:10.1007/s11464-015-0435-5

Front. Math. China

2015, Vol. 10

Issue (3) : 547-565 https://doi.org/10.1007/s11464-015-0435-5

RESEARCH ARTICLE

Map composition generalized to coherent collections of maps

Herng Yi CHENG¹,Kang Hao CHEONG^1,^2,^*(

)

1. National University of Singapore High School of Mathematics and Science, Singapore 129957, Singapore
2. Tanglin Secondary School, Singapore 127391, Singapore

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Abstract

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.

Keywords Relation algebra partial algebra composition

Corresponding Author(s): Kang Hao CHEONG

Issue Date: 01 April 2015

Cite this article:

Herng Yi CHENG,Kang Hao CHEONG. Map composition generalized to coherent collections of maps[J]. Front. Math. China, 2015, 10(3): 547-565.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0435-5
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I3/547

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