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Lawvere Completion and Separation Via Closure

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Abstract

For a quantale \(\mathsf{V}\), first a closure-theoretic approach to completeness and separation in \(\mathsf{V}\text{-categories}\) is presented. This approach is then generalized to , where is a topological theory that entails a set monad \( \mathbb{T}\) and a compatible \( \mathbb{T}\text{-algebra}\) structure on \(\mathsf{V}\).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    Dirk Hofmann

  2. Department of Mathematics and Statistics, York University, M3J 1P3, Toronto, Ontario, Canada

    Walter Tholen

Authors
  1. Dirk Hofmann
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  2. Walter Tholen
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Correspondence to Dirk Hofmann.

Additional information

Dedicated to Bill Lawvere at the occasion of his seventieth birthday.

The first author acknowledges partial financial assistance by Unidade de Investigação e Desenvolvimento Matemática e Aplicações da Universidade de Aveiro/FCT.

The second author acknowledges partial financial assistance by the Natural Sciences and Engineering Council of Canada.

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Hofmann, D., Tholen, W. Lawvere Completion and Separation Via Closure. Appl Categor Struct 18, 259–287 (2010). https://doi.org/10.1007/s10485-008-9169-9

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  • DOI: https://doi.org/10.1007/s10485-008-9169-9

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