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Order completion monads

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Abstract

Categories of partially ordered sets that are complete under least upper bounds of subsets of a given form (finite, chains, etc.) are characterized as categories of algebras for submonads of the monad of complete semilattices. A general completion construction is given, and several structural properties, such as tensor products, colimits, and factorizations, are studied.

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Authors and Affiliations

  1. SRI International, Menlo Park, California, USA

    J. Meseguer

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  1. J. Meseguer
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MEC (Spain) postdoctoral research fellow. On leave from Dto. Algebra y Fund., Universidad de Santiago. Research conducted at the Mathematics Department, University of California at Berkeley.

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Meseguer, J. Order completion monads. Algebra Universalis 16, 63–82 (1983). https://doi.org/10.1007/BF01191754

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