On the concrete representation of discrete enriched abstract clones
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Authors
Fiore, MP
Publication Date
2017-06-01Journal Title
Tbilisi Mathematical Journal
ISSN
1875-158X
Publisher
Tbilisi Centre for Mathematical Sciences
Volume
10
Issue
3
Pages
297-328
Type
Article
Metadata
Show full item recordCitation
Fiore, M. (2017). On the concrete representation of discrete enriched abstract clones. Tbilisi Mathematical Journal, 10 (3), 297-328. https://doi.org/10.1515/tmj-2017-0115
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.
Identifiers
External DOI: https://doi.org/10.1515/tmj-2017-0115
This record's URL: https://www.repository.cam.ac.uk/handle/1810/285498
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
Licence URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
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