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The category of complete lattices as a category of algebras

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Abstract

Complete lattices are regarded as algebras whose operations are joins and meets of arbitary arities. We show that, unlike algebras of classical algebraic theories, they admit implicit operations (operations compatible with homomorphisms) which are not induced by terms and that there are more than a proper class of such “wild” operations. We show how they are related to terms.

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  1. Katedra matematiky FJFI CVUT, Trojanova 3, 12000, Praha 2, Czechoslovakia

    Jan Reiterman

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  1. Jan Reiterman
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In Memory of Evelyn Nelson

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Reiterman, J. The category of complete lattices as a category of algebras. Algebra Universalis 26, 367–379 (1989). https://doi.org/10.1007/BF01211843

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  • DOI: https://doi.org/10.1007/BF01211843

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