On the concrete representation of discrete enriched abstract clones

Authors
Fiore, MP 

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Article
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Abstract

We consider discrete enriched abstract clones and provide two constructions investigating their representation as discrete enriched clones of operations on objects in concrete enriched cate- gories over the enriching category. Our first construction embeds a discrete enriched abstract clone into the concrete discrete enriched clone of operations on an object in the enriching cate- gory. Our second construction refines the given embedding by introducing a monoid action and restricting attention to the concrete discrete enriched clone of its equivariant operations. As in the classical theory of abstract clones, our main focus is on discrete enriched abstract clones with finite arities. However, we also consider discrete enriched abstract clones with countable arities to show that the representation theory of the former is conceptually explained by that of the latter.

Publication Date
2017-06-01
Online Publication Date
2017-12-27
Acceptance Date
2017-11-26
Keywords
4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Tbilisi Mathematical Journal
Journal ISSN
1875-158X
1512-0139
Volume Title
10
Publisher
Tbilisi Centre for Mathematical Sciences