Injective Hulls of Quantale-Enriched Multicategories

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Abstract

In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, we show that every quantale-enriched multicategory admits an injective hull. Finally, we expose a connection between the Isbell adjunction and the construction of injective hulls for topological spaces made by Banaschewski in 1973.

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    In particular \(a((-), y) = a(u_X, y)\).

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Acknowledgements

I am grateful to D. Hofmann for valuable discussions about the content of the paper and to I. Stubbe for the valuable suggestions he gave me during his visit to Aveiro. The author would like to thank the anonymous referee who kindly reviewed the earlier version of this manuscript and provided valuable suggestions and comments which lead to an overall improvement of the paper.

The author acknowledges partial financial assistance by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947, and project UID/MAT/04106/2019 (CIDMA). The author is also supported by FCT grant PD/BD/128187/2016.

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Correspondence to Eros Martinelli.

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The original online version of this article was revised: An author contribution section that was inadvertently included in the original article was removed.

Communicated by Maria Manuel Clementino.

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Martinelli, E. Injective Hulls of Quantale-Enriched Multicategories. Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09650-0

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Keywords

  • Quantales
  • Quantale-enriched categories
  • Injective objects
  • Injective hulls
  • Quantale-enriched multicategories