Finitary monads on the category of posets

Finitary monads on Pos are characterized as precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequations in context. Analogously, finitary enriched monads on Pos are characterized: here we work with varieties of coherent algebras which me...

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Bibliographic Details
Published in:Mathematical structures in computer science 2021-08, Vol.31 (7), p.799-821
Main Authors: Adámek, Jiří, Ford, Chase, Milius, Stefan, Schröder, Lutz
Format: Article
Language:English
Subjects:
Algebra
Computer science
Set theory
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Summary:Finitary monads on Pos are characterized as precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequations in context. Analogously, finitary enriched monads on Pos are characterized: here we work with varieties of coherent algebras which means that their operations are monotone.
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129521000360